1. K-theory Preprint Archives Electronic preprint archives for mathematics research papers in ktheory. http://www.math.uiuc.edu/K-theory/

K-theory Preprint Archives Welcome to the preprint archives for papers in K-theory. We accept submissions of preprints in electronic form for storage until publication. Storage after publication may be possible, too. RSS feed for K-theory preprints Search with google: Our mirror site in Germany Our home site in the USA Instructions for authors Instructions for joining the mailing list. Members of the mailing list receive announcements of preprints when they are deposited in the archives. (The list has more than 300 members.) Best Current Practices: Recommendations on Electronic Information Communication A calendar of K-theory events. A bibtex file (2342698 bytes), or the same thing gzipped (557172 bytes) containing 6454 citations to papers related to K-theory and instructions for enlarging bibtex to work with such a large file. MPRESS , a searchable index of preprints, including references to the preprints stored here. Some TeX fonts , stored in a tar image compressed with gzip, including the lams* and xy* fonts, which are needed for some of the preprints. The unprocessed recent submissions bibtex entries Related sites: K-theory Front for the arXiv Preprints: SFB 343 "Diskrete Strukturen in der Mathematik" TMR Network: Algebraic K-Theory, Linear Algebraic Groups and Related Structures

2. K-theory - Wikipedia, The Free Encyclopedia In mathematics, ktheory is a tool used in several disciplines. In algebraic topology, it is an extraordinary cohomology theory known as topological http://en.wikipedia.org/wiki/K-theory

K-theory From Wikipedia, the free encyclopedia Jump to: navigation search In mathematics K-theory is a tool used in several disciplines. In algebraic topology , it is an extraordinary cohomology theory known as topological K-theory . In algebra and algebraic geometry , it is referred to as algebraic K-theory . It also has some applications in operator algebras . It leads to the construction of families of K functors , which contain useful but often hard-to-compute information. In physics , K-theory and in particular twisted K-theory have appeared in Type II string theory where it has been conjectured that they classify D-branes Ramond-Ramond field strengths and also certain spinors on generalized complex manifolds . For details, see also K-theory (physics) edit Early history The subject was originally discovered by Alexander Grothendieck (1957) so that he could formulate his Grothendieck-Riemann-Roch theorem . It takes its name from the German "Klasse", meaning "class" . Grothendieck needed to work with sheaves on an algebraic variety X . Rather than working directly with the sheaves, he gave two constructions. In the first, he used the operation of direct sum to convert the commutative

3. Lectures On Topological K-theory This will be an expository seminar on the elements of topological ktheory at a level suitable for graduate students in mathematics and physics. http://online.kitp.ucsb.edu/online/ktheory/

Home Activities Inside KITP Directory ... UCSB Mar 30, 2008 Lectures on Topological K-theory ITP Small Seminar Room Fridays at 3:30 pm, Spring 2000 Friday, April 7, Xianzhe Dai, Introduction [Audio] Friday, April 14, Siye Wu, The Grothendieck construction [Audio] Friday, April 21, Bill Jacob, Algebraic K-theory (first steps) [Audio] Friday, April 28, Doug Moore, K-theory and cohomology Friday, May 5, Rick Ye, The Bott periodicity theorem [Audio] Friday, May 12, Joe Polchinski, D-branes and K-theory [Audio] Friday, May 19, Simeon Hellerman, D-branes and K-theory II [Audio] Friday, May 26, Morten Krogh, Ramond-Ramond fields and K-theory I [Audio] Friday, June 2, Morten Krogh, Ramond-Ramond fields and K-theory II [Audio] Friday, June 9, Siye Wu, K-theory, T-duality and D-brane anomalies [Audio] This will be an expository seminar on the elements of topological K-theory at a level suitable for graduate students in mathematics and physics. Just like the fundamental group and the de Rham cohomology groups, K-theory provides topological invariants of smooth manifolds. These topological invariants are constructed from isomorphism classes of vector bundles over manifolds. Among its early applications to topology was a simple proof of the fact that the only spheres which possess trivial tangent bundles are those of dimensions 1,3 and 7. It was also one of the key tools used by Atiyah and Singer in their index theorem for systems of elliptic partial differential equations on smooth manifolds. More recently K-theory has become an important ingredient in the theory of D-branes from theoretical physics.

4. An Introduction To Algebraic K-theory An introduction to algebraic ktheory by Charles Weibel. Chapters in DVI. http://www.math.rutgers.edu/~weibel/Kbook.html

``The K-book: An introduction to algebraic K-theory'' by Charles Weibel (a graduate textbook in progress) Introduction here Chapter I : Projective Modules and Vector Bundles Here is the searchable PDF file Last major update March 1997 (section 4). Minor updates July 2000, Sept. 2004, June 2005, May 2007. 1. Free and stably free modules; p.1 2. Projective modules; p.6 3. The Picard group of a ring; p.15 4. Topological vector bundles and Chern classes; p.26 5. Algebraic vector bundles. p.38 Chapter II : The Grothendieck group K_0 (101 pp.) Here is the searchable PDF file Last major updates Dec. 2003 (sec.6, 7, 9), July 2004 (sec.2, 7, App.). Minor updates Sept. 2004, June 2005 (sec.3), August 2006 (Burnside ring), Jan 2007 (compatibility with Chapter V). 1. group completion of a monoid; p.1 2. K_0 of a ring; p.5 3. K(X) of a topological space; p.17 Lambda and Adams operations; p.24 5. K_0 of a symmetric monoidal category; p.37 6. K_0 of an abelian category; p.45 7. K_0 of an exact category; p.59 8. K_0 of schemes and varieties; p.73

5. 19: K-theory Encyclopedic reference for ktheory in Dave Rusin s Mathematical Atlas. Includes a brief history along with various links to textbooks, reference works, http://www.math.niu.edu/~rusin/known-math/index/19-XX.html

Search Subject Index MathMap Tour ... Help! ABOUT: Introduction History Related areas Subfields POINTERS: Texts Software Web links Selected topics here 19: K-theory Introduction K-theory is an interesting blend of algebra and geometry. Originally defined for (vector bundles over) topological spaces it is now also defined for (modules over) rings, giving extra algebraic information about those objects. History Read Atiyah's, "K-Theory Past and Present" at here Applications and related fields Most of the geometric K-theory is treated with Algebraic Topology See also 16E20, 18F25 Subfields Grothendieck groups and K_0, see also 13D15, 18F30 Whitehead groups and K_1 Steinberg groups and K_2 Higher algebraic K-theory K-theory in geometry K-theory in number theory, see also 11R70, 11S70 K-theory of forms, see also 11EXX Obstructions from topology K-theory and operator algebras See mainly 46L80, and also 46M20 Topological K-theory, see also 55N15, 55R50, 55S25 Miscellaneous applications of K-theory K-Theory is the smallest of the 61 active areas of the MSC scheme: only 515 papers with primary classification 19-XX during 1980-1997. But the area 19-XX was only available as a primary classification for Math Reviews papers starting with MR96; hence the count above is an undercount of the true size of the field. (Even granting this, however, K-theory is a fairly small field.) Browse all (old) classifications for this area at the AMS.

6. Vector Bundles & K-Theory Book The plan is for this to be a fairly short book focusing on topological ktheory and containing also the necessary background material on vector bundles and http://www.math.cornell.edu/~hatcher/VBKT/VBpage.html

The plan is for this to be a fairly short book focusing on topological K-theory and containing also the necessary background material on vector bundles and characteristic classes. Here is a provisional Table of Contents At present about half of the book is in good enough shape to be posted online, approximately 110 pages. What is included in this installment is: Chapter 1, containing basics about vector bundles. Part of Chapter 2, introducing K-theory, then proving Bott periodicity in the complex case and Adams' theorem on the Hopf invariant, with its famous applications to division algebras and parallelizability of spheres. Not yet written is the proof of Bott Periodicity in the real case, with its application to vector fields on spheres. Most of Chapter 3, constructing Stiefel-Whitney, Chern, Euler, and Pontryagin classes and establishing their basic properties. Part of Chapter 4 on the stable J-homomorphism. What is written so far is just the application of complex K-theory, using the Chern character, to give a lower bound on the order of the image of the stable J-homomorphism. Much of this material is already well covered in other sources, notably the classic books of Atiyah (

7. SpringerLink - Journal springerlink.metapress.com/content/15730514/ - k-theory - Algebra. This journal is devoted to developments in the mathematical sciences that are related to one of the various aspects of k-theory. http://springerlink.metapress.com/content/1573-0514/

var isIE = false; Athens Authentication Point Welcome! To use the personalized features of this site, please log in or register If you have forgotten your username or password, we can help My Menu Marked Items Alerts Order History Saved Items All Favorites Content Types All ... Professional Computing and Web Design English Deutsch Journal K-Theory Publisher Springer Netherlands ISSN 0920-3036 (Print) 1573-0514 (Online) Subject Collection Mathematics and Statistics Subject Mathematics and Statistics Mathematics Algebra Analysis ... Geometry and Group Theory and Generalizations SpringerLink Date Friday, April 05, 2002 Add to marked items Add to saved items Register for TOC Alerting Recommend this journal ... Manuscript Submission Editorial View Condensed List View Expanded List View 38 Volumes First Page Next Page Current-34 Access to all content Access to some content Access to no content Volume 38 Number 2 / January, 2008

8. K-Theory -- From Wolfram MathWorld Topological K theory is significant because it forms a generalized cohomology theory, and it leads to a solution to the vector fields on spheres problem, http://mathworld.wolfram.com/K-Theory.html

Algebra Applied Mathematics Calculus and Analysis Discrete Mathematics ... Budney K-Theory A branch of mathematics which brings together ideas from algebraic geometry linear algebra , and number theory . In general, there are two main types of -theory: topological and algebraic. Topological -theory is the "true" -theory in the sense that it came first. Topological -theory has to do with vector bundles over topological spaces . Elements of a -theory are stable equivalence classes of vector bundles over a topological space . You can put a ring structure on the collection of stably equivalent bundles by defining addition through the Whitney sum , and multiplication through the tensor product of vector bundles . This defines "the reduced real topological -theory of a space." "The reduced -theory of a space" refers to the same construction, but instead of real vector bundles complex vector bundles are used. Topological -theory is significant because it forms a generalized cohomology theory, and it leads to a solution to the vector fields on spheres problem, as well as to an understanding of the -homeomorphism of homotopy theory Algebraic -theory is somewhat more involved. Swan (1962) noticed that there is a correspondence between the

9. K-Theory And Homology Authors/titles Recent Submissions KT); Functional Analysis (math.FA); Group Theory (math.GR) Subjects Rings and Algebras (math.RA); ktheory and Homology (math.KT) http://arxiv.org/list/math.KT/recent

arXiv.org math math.KT Search or Article-id Help Advanced search All papers Titles Authors Abstracts Full text Help pages K-Theory and Homology Authors and titles for recent submissions Mon, 31 Mar 2008 Fri, 28 Mar 2008 Thu, 27 Mar 2008 Wed, 26 Mar 2008 ... Tue, 25 Mar 2008 [ total of 9 entries: [ showing up to 25 entries per page: fewer more Mon, 31 Mar 2008 arXiv:0803.4168 ps pdf other Title: Relative differential K-characters Authors: Mohamed Maghfoul Comments: Published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at this http URL Journal-ref: SIGMA 4 (2008), 035, 10 pages Subjects: K-Theory and Homology (math.KT) ; Algebraic Topology (math.AT) arXiv:0803.4136 pdf other Title: Homological stability for certain classical groups Authors: Jan Essert Subjects: K-Theory and Homology (math.KT) Fri, 28 Mar 2008 arXiv:0803.3907 (cross-list from math.RT) [ ps pdf other Title: Grothendieck Group and Generalized Mutation Rule for 2-CalabiYau Triangulated Categories Authors: Yann Palu (IMJ) Subjects: Representation Theory (math.RT) ; Category Theory (math.CT); K-Theory and Homology (math.KT)

10. Not Even Wrong » Blog Archive » Another Journal Board Resigns Ars Mathematica » Blog Archive » ktheory editorial board resigns Says Woit reports that the entire editorial board of the journal k-theory (published http://www.math.columbia.edu/~woit/wordpress/?p=581

11. Front: Math.KT K-Theory And Homology arXiv0803.1635 Poisson (co)homology of polynomial Poisson algebras in dimension four Sklyanin s case. Serge Romeo Tagne Pelap. math.KT. http://front.math.ucdavis.edu/math.KT

Front for the arXiv Fri, 28 Mar 2008 Front math KT search register submit journals ... iFAQ math.KT K-Theory and Homology Calendar Search Atom feed Search Author Title/ID Abstract+ Category articles per page Show Search help Recent New articles (last 12) 27 Mar arXiv:0803.3655 Free products, cyclic homology, and the Gauss-Manin connection. Victor Ginzburg , Travis Schedler math.KT math.AG math.QA 27 Mar arXiv:0803.3689 Cohomology of twisted tensor products. Petter Andreas Bergh , Steffen Oppermann math.KT math.QA 27 Mar arXiv:0803.3669 Deforming motivic theories I: Pure weight perfect Modules on divisorial schemes. Toshiro Hiranouchi , Satoshi Mochizuki math.KT 26 Mar arXiv:0803.3550 Hochschild homology and global dimension. Petter Andreas Bergh , Dag Madsen math.KT math.RA 20 Mar arXiv:0803.2781 Functoriality of the canonical fractional Galois ideal. Paul Buckingham , Victor Snaith math.KT Cross-listings 28 Mar arXiv:0803.3907 Grothendieck Group and Generalized Mutation Rule for 2-CalabiYau Triangulated Categories. Yann Palu (IMJ). math.RT math.CT math.KT 27 Mar arXiv:0803.3798

12. The Math Forum - Math Library - K-Theory The Math Forum s Internet Math Library is a comprehensive catalog of Web sites and Web pages relating to the study of mathematics. This page contains sites http://mathforum.org/library/topics/k_theory/

Browse and Search the Library Home Math Topics Algebra Modern Algebra : K-Theory Library Home Search Full Table of Contents Suggest a Link ... Library Help Selected Sites (see also All Sites in this category K-Theory - Dave Rusin; The Mathematical Atlas A short article designed to provide an introduction to K-theory, a blend of algebra and geometry. Originally defined for (vector bundles over) topological spaces it is now also defined for (modules over) rings, giving extra algebraic information about those objects. History; applications and related fields and subfields; textbooks, reference works, and tutorials; software and tables; other web sites with this focus. more>> All Sites - 8 items found, showing 1 to 8 arXiv.org e-Print archive - Los Alamos National Laboratory (LANL) A major site for mathematics preprints that has incorporated many formerly independent specialist archives including alg-geom, funct-an, dg-ga, q-alg, auto-fms, cd-hg, MAGNUS, Several Complex Variables, Logic E-prints, Commutative Algebra, Dynamical Systems, ...more>> Front for the Mathematics ArXiv - Univ. of California, Davis

13. K-theory -- Britannica Online Encyclopedia He was one of the pioneers, along with the Frenchman Alexandre Grothendieck and the German Friedrich Hirzebruch, in the development of ktheory—culminating http://www.britannica.com/eb/topic-309101/K-theory

document.writeln(''); document.writeln('Initializing application...'); Username Password Remember me Forgot your password? Browse Shop Log In Search Site: K-theory mathematics Main Aspects of this topic are discussed in the following places at Britannica. Assorted References algebraic topology in mathematics: Mathematical physics and the theory of groups ...in the 1960s, work chiefly by Grothendieck and the English mathematician Michael Atiyah showed how the study of vector bundles on spaces could be regarded as the study of cohomology theory (called K theory). More significantly still, in the 1960s Atiyah, the American Isadore Singer, and others found ways of connecting this work to the study of a wide variety of questions involving partial... work of Atiyah in Atiyah, Sir Michael Francis ...in Moscow in 1966 for his work on topology and analysis. He was one of the pioneers, along with the Frenchman Alexandre Grothendieck and the German Friedrich Hirzebruch, in the development of K Citations MLA Style: K-theory http://www.britannica.com/bps/topic/309101/K-theory

14. PlanetMath: Algebraic K-theory Algebraic ktheory is a series of functors on the category of rings. Broadly speaking, it classifies ring invariants, i.e. ring properties that are Morita http://planetmath.org/encyclopedia/AlgebraicKTheory.html

(more info) Math for the people, by the people. Encyclopedia Requests Forums Docs ... RSS Login create new user name: pass: forget your password? Main Menu sections Encyclop¦dia Papers Books Expositions meta Requests Orphanage Unclass'd Unproven ... Classification talkback Polls Forums Feedback Bug Reports downloads Snapshots PM Book information News Docs Wiki ChangeLog ... About Algebraic K-theory (Topic) Algebraic K-theory is a series of functors on the category of rings . Broadly speaking, it classifies ring invariants , i.e. ring properties that are Morita invariant The functor Let be a ring and denote by the algebraic direct limit of matrix algebras under the embeddings . The zeroth K-group of , is the Grothendieck group abelian group of formal differences ) of idempotents in up to similarity transformations . Let and be two idempotents. The sum of their equivalence classes and is the equivalence class of their direct sum where . Equivalently, one can work with finitely generated projective modules over The functor Denote by the direct limit of general linear groups under the embeddings . Give the direct limit topology , i.e. a

15. K-Theory For Dummies, II | The String Coffee Table Before finishing the last entry I should review some basic facts about ktheory and D-branes, beyond of what I had in my previous notes ( ). http://golem.ph.utexas.edu/string/archives/000880.html

@import url("/string/styles-site.css"); The String Coffee Table A Group Blog on Physics Skip to the Main Content Enough, already! Skip to the content. Note: These pages make extensive use of the latest XHTML and CSS Standards only supported in Mozilla. My best suggestion (and you will thank me when surfing an ever-increasing number of sites on the web which have been crafted to use the new standards) is to upgrade to the latest version of your browser. If that's not possible, consider moving to the Standards-compliant and open-source Mozilla browser. Main July 26, 2006 K-Theory for Dummies, II Posted by Urs Schreiber Before finishing the last entry I should review some basic facts about K-theory and D-branes, beyond of what I had in my previous notes ( Apart from the Brodzki-Mathai-Rosenberg-Szabo paper ( T. Asakawa, S. Sugimoto, S. Terashima D-branes, Matrix Theory and K-homology hep-th/0108085 which is based in part on Richard J. Szabo Superconnections, Anomalies and Non-BPS Brane Charges hep-th/0108043 and Jeffrey A. Harvey, Gregory Moore Noncommutative Tachyons and K-Theory hep-th/0009030 Edward Witten Overview Of K-Theory Applied To Strings hep-th/0007175 several refinements of the precise relationship have been discussed. Usually, the decategorification and Grothedieck group completion performed in forming K-theory from the category of vector bundles is identified with the physical process of partial mutual annihilation of space-filling D9 brane and anti-brane pairs, thereby realizing all lower-dimensional branes as decay products of D9-brane configurations.

16. Milnor, J.: Introduction To Algebraic K-Theory. (AM-72). of the book Introduction to Algebraic ktheory. (AM-72) by Milnor, J., published by Princeton University Press....... http://press.princeton.edu/titles/1568.html

Book Search: Keywords Author Title or ISBN More Options Power Search Search Hints Google contents of this website: Google full text of our books: Introduction to Algebraic K-Theory. (AM-72) John Milnor 200 pp. Shopping Cart Google full text of this book: Other Princeton books by John Milnor: Characteristic Classes. (AM-76). Dynamics in One Complex Variable: Third Edition. (AM-160). Morse Theory. (AM-51). Prospects in Mathematics. (AM-70). ... Topology from the Differentiable Viewpoint. Series: Annals of Mathematics Studies Phillip A. Griffiths, John N. Mather, and Elias M. Stein, Editors Subject Area: Mathematics VISIT OUR MATH WEBSITE Paper: Not for sale in Japan Shopping Cart: For customers in the U.S., Canada, Latin America, Asia, and Australia Paper: $45.00 ISBN13: 978-0-691-08101-4 For customers in Europe, Africa, the Middle East, and India Prices subject to change without notice File created: 2/26/2008 Questions and comments to: webmaster@press.princeton.edu Princeton University Press New Book E-Mails New In Print Subjects Catalogs ... PUP Home Send me emails about new books in: Mathematics More Choices Email: Country: Name:

17. K-Theory And Homology Authors/titles Recent Submissions Comments To appear on the Proceedings of the International Conference on ktheory and Non commutative geometry , VASBI, held at Valladolid Spain, http://aps.arxiv.org/list/math.KT/recent

aps.arXiv.org math math.KT Search or Article-id Help Advanced search All papers Titles Authors Abstracts Full text K-Theory and Homology Authors and titles for recent submissions Fri, 28 Mar 2008 Thu, 27 Mar 2008 Wed, 26 Mar 2008 Tue, 25 Mar 2008 ... Thu, 20 Mar 2008 [ total of 9 entries: [ showing up to 25 entries per page: fewer more Fri, 28 Mar 2008 arXiv:0803.3907 (cross-list from math.RT) [ ps pdf other Title: Grothendieck Group and Generalized Mutation Rule for 2-CalabiYau Triangulated Categories Authors: Yann Palu (IMJ) Subjects: Representation Theory (math.RT) ; Category Theory (math.CT); K-Theory and Homology (math.KT) Thu, 27 Mar 2008 arXiv:0803.3689 ps pdf other Title: Cohomology of twisted tensor products Authors: Petter Andreas Bergh Steffen Oppermann Comments: 10 pages Subjects: K-Theory and Homology (math.KT) ; Quantum Algebra (math.QA) arXiv:0803.3669 ps pdf other Title: Deforming motivic theories I: Pure weight perfect Modules on divisorial schemes Authors: Toshiro Hiranouchi Satoshi Mochizuki Subjects: K-Theory and Homology (math.KT) arXiv:0803.3655

18. JSTOR Algebraic And Etale $K$-Theory We define etale ktheory, interpret various conjectures of Quillen and Lichtenbaum in terms of a map from algebraic k-theory to etale k-theory, http://links.jstor.org/sici?sici=0002-9947(198511)292:1<247:AAE>2.0.CO;2-T

19. Cambridge Journals Online - Journal Of K-Theory Journal of ktheory is concerned with developments and applications of ideas and methodologies called k-theory. They have their origin in the work of http://journals.cambridge.org/action/displayJournal?jid=KAG

20. Noncommutative Geometry: The Editorial Board Of 'K-Theory' Has Resigned. of ktheory has been established. In recent years `k-theory was published by Springer. `Journal of k-theory will be published by the Cambridge University http://noncommutativegeometry.blogspot.com/2007/08/editorial-board-of-k-theory-h

skip to main skip to sidebar Noncommutative geometry Blog Archive December Noncommutative Geometry in China October HEART BIT # 1 ... test post 1: atom feeds Events Le mod¨le spectral; Course by Alain Connes, 10 janvier- 6 mars 2008; Coll¨ge de France THE SIXTH ANNUAL SPRING INSTITUTE ON NONCOMMUTATIVE GEOMETRY AND OPERATOR ALGEBRAS, May 5-14 2008 Noncommutative geometry and geometry over the field with one element May 15-18, 2008 Trimester Program on Geometry and Physics, May - August 2008, Hausdorff Research Institute for Mathematics, Bonn, Germany ... Algebraic and Geometric Deformation Spaces, Max-Planck Institute, Bonn, August 11-15, 2008 Positions available (New!) Maitre de Conference at Laboratoire de math©matiques et applications de Metz Postdoc Positions in Mathematics (Copenhagen) Tenure-Track Professorships at Courant Research Centre, Goettingen PhD position on integration theory in quantum group theory and noncommutative geometry, Radboud University in Nijmegen Links Journal of Noncommutative Geometry The n-Category Caf© Not Even Wrong Never Ending Books ... Vivatsgasse 7 Past Events Workshop on Noncommutative Geometry, Copenhagen, Feb 25-29, 2008

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