1. Algebraic Topology - Wikipedia, The Free Encyclopedia Retrieved from http//en.wikipedia.org/wiki/algebraic_topology . Categories Topology Algebraic topology Abstract algebra http://en.wikipedia.org/wiki/Algebraic_topology

Algebraic topology From Wikipedia, the free encyclopedia Jump to: navigation search For the topology of pointwise convergence, see Algebraic topology (object) Algebraic topology is a branch of mathematics in which tools from abstract algebra are used to study topological spaces Contents The method of algebraic invariants Results on homology Setting in category theory Applications of algebraic topology ... edit The method of algebraic invariants The goal is to take topological spaces and further categorize or classify them. An older name for the subject was combinatorial topology , implying an emphasis on how a space X was constructed from simpler ones (the modern standard tool for such construction is the CW-complex ). The basic method now applied in algebraic topology is to investigate spaces via algebraic invariants, by mapping them, for example, to groups which have a great deal of manageable structure in a way that respects the relation of homeomorphism of spaces. This allows one to recast statements about topological spaces into statements about groups, which are often easier to prove. Two major ways in which this can be done are through fundamental groups , or more generally homotopy theory , and through homology and cohomology groups. The fundamental groups give us basic information about the structure of a topological space, but they are often

2. CiteULike: Tag Algebraic_topology [10 Articles] Recent papers classified by the tag algebraic_topology. posted to algebraic_topology by NitinCR on 200705-09 191722 as http://www.citeulike.org/tag/algebraic_topology

Register Log in FAQ Sponsored link CiteULike News CiteGeist Discussion Journals Browse current issues Groups Search groups Tag algebraic_topology [10 articles] Recent papers classified by the tag algebraic_topology. Simplicial Objects in Algebraic Topology (Chicago Lectures in Mathematics) (15 January 1993) by JP May posted to by NitinCR on 2007-05-09 19:17:22 as A Concise Course in Algebraic Topology (Chicago Lectures in Mathematics) (01 September 1999) by JP May posted to by NitinCR on 2007-05-09 19:17:04 as Algebraic Topology: An Intuitive Approach (Translations of Mathematical Monographs) (10 June 1999) by Hajime Sato posted to by NitinCR on 2007-05-11 10:34:08 as Algebraic Topology (15 November 2001) by Allen Hatcher posted to by NitinCR on 2007-05-08 05:36:34 as along with 1 person mmarcus Algebraic Topology (05 September 1997) by William Fulton posted to by NitinCR on 2007-11-30 21:46:21 as Algebraic Topology (14 June 1996) by CRF Maunder posted to by NitinCR on 2007-05-09 19:16:59 as A Basic Course in Algebraic Topology (Graduate Texts in Mathematics) (29 May 1997) by William S Massey posted to by NitinCR on 2007-05-07 06:51:13 as Lectures on Algebraic Topology (Classics in Mathematics) (15 February 1995) by Albrecht Dold , A Dold posted to by NitinCR on 2007-05-06 15:55:45 as Algebraic topology by Allen Hatcher posted to textbook by eibin to the group NoncommutativeGeometry on 2006-01-20 02:18:54 as along with 1 person pweil Lecture notes in algebraic topology Vol. 35 (2001)

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4. Matematicas-hatcher-algebraic_topology - ESnips, Share Anything (En inglés) Libro de Topología Algebraica. En esta carpeta puedes hallar otro en español cuya autora es Marta Macho. http://www.esnips.com/doc/6d44aa65-9ae2-4ccb-9314-3a5186ab1a1c/matematicas-hatch

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5. Algebraic_topology Henri Poincare; Algebraic Topology Discussion List; Topics in Topology; University of Glasgow; Allen Hatcher s online Algebraic Topology book http://infohost.nmt.edu/~jstarret/algebraic_topology.html

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Web Shopping Articles Local ... Search Engine Marketing Search for: in: All The Internet Images Google Yahoo Altavista Fast Ask Jeeves Lycos MSN Wisenut Hotbot AOL Search Teoma Home Internet Search Directory Shopping Search Local Search ... Search Engine Marketing Algebraic Topology Home Science Math Topology Sites in Algebraic Topology Algebraic K-theory, Groups and Categories Report of a research programme at the University of Wales, Bangor. http://www.bangor.ac.uk/~mas010/intasrep.html Algebraic Topology In Dave Rusin's Mathematical Atlas. http://www.math.niu.edu/~rusin/known-math/index/55-XX.html Algebraic Topology Discussion List Information on subscribing, archives of past discussions, and links to home pages of algebraic topologists. http://www.lehigh.edu/dmd1/public/www-data/algtop.html Algebraic Topology and Concurrency Applications of algebraic topology to computer science. http://www.ipipan.gda.pl/~stefan/AlgTop/ Algebraic Topology by Solomon Lefschetz Published by the AMS, available for free download as PDF files. http://www.ams.org/online_bks/coll27/

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9. University Of Glasgow :: Mathematics :: Algebraic_topology Home Departments Mathematics Research algebraic_topology. Mathematics. Research. Algebra; Analysis; Fluid Dynamics MHD; Geometry Topology http://www.gla.ac.uk/departments/mathematics/research/algebraictopology/

@import "http://www.gla.ac.uk/t4/generic/ss/standard.css"; @import "http://www.gla.ac.uk/t4/generic/ss/nav.css"; @import "http://www.gla.ac.uk/t4/generic/ss/fims.css"; @import "http://www.gla.ac.uk/t4/maths/ss/local.css"; A-Z : ACADEMIC DEPARTMENTS SERVICES STAFF UNIVERSITY of GLASGOW Mathematics Part of the Faculty of Information and Mathematical Sciences Home Departments Mathematics ... Publications Algebraic Topology Geometry and Algebraic Topology play major roles throughout Mathematics and its applications, with geometric and topological ideas often being indispensable. Algebraic Topology has developed important machinery such as cohomology theories including ordinary cohomology, K-theory, cobordism and elliptic cohomology. These are often of use in geometric situations, as well as within Algebraic Topology; Algebraic Topologists tend to study much less `rigid' geometric situations than other Geometers.There have also been significant interactions with many areas of Algebra, and indeed much of Algebraic Topology can be viewed as `applied algebra' as well as being a major source of innovative algebraic ideas. In the words of Hermann Weyl: ` In these days the angel of topology and the devil of abstract algebra fight for the soul of every individual discipline of mathematics Departmental research activity in Topology occurs in the following areas.

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Directory Submit Site Free Advertising Sign In ... Sponsor This Category Free for 60 Days - Customize your message and appear alongside search results. Start your Free Trial today! Top: Science: Math: Topology: ... Algebraic K-theory, Groups and Categories - Provides research areas, activities, collaborations, and problems encountered. Algebraic Topology - Presents an explanation regarding the method of algebraic invariants. With articles and discussion of various topics. Algebraic Topology - Provides the algebraic tools, a history, and the applications and related fields. Algebraic Topology and Concurrency - Information includes a complete listing of reports. Also presents books and their respective authors. Algebraic Topology Discussion List - Provides information on topology conferences, and serving as a forum for topics related to algebraic topology. With a list of e-mail addresses of the people on the list. Algorithms for the Fixed Point Property - Presents a survey that exhibits various algorithms. Includes a discussion on reduction theorems and references. British Topology Home Page - Shows some pointers to topology-related sites. With resources, groups, and galleries.

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18. Algebraic Topology A branch of topology that deals with invariants of a topological space which are algebraic structures, often groups. Related categories • TOPOLOGY http://www.daviddarling.info/encyclopedia/A/algebraic_topology.html

TOPOLOGY MATHEMATICS A B ... CONTACT entire Web this site algebraic topology A branch of topology that deals with invariants of a topological space which are algebraic structures, often groups Related categories TOPOLOGY MATHEMATICS Also on this site: Encyclopedia of History BACK TO TOP var site="s13space1234"

19. Algebraic Topology - Wikipedia Algebraic topology. Algebraic topology is a branch of mathematics in which tools from abstract algebra are used to study topological spaces. http://facetroughgemstones.com/wikipedia/al/Algebraic_topology.html

Office Supplies Buy Posters A-Z Products Website Advertising ... Algebraic topology Algebraic topology is a branch of mathematics in which tools from abstract algebra are used to study topological spaces The goal is to take topological spaces, and further categorize them by mapping them to groups , which have a great deal of structure. Two major ways in which this can be done are through fundamental groups , or homotopy, and through homology /cohomology groups. Fundamental groups give us crucial information about the structure of a topological space, but they are often nonabelian and can be difficult to work with. Homology/Cohomology groups, on the other hand, are abelian, and in many important cases even finitely generated. Finitely generated abelian groups can be completely classified and are particularly easy to work with. Several nice results follow immediately from working with finitely generated abelian groups . If an n -th homology group of a simplicial complex has torsion, then the complex is nonorientable . The free rank of the n -th homology group of a simplicial complex is equal to the n -th Betti number[?]

20. Algebraic Topology - AoPSWiki Retrieved from http//www.artofproblemsolving.com/Wiki/index.php/algebraic_topology . Categories Incomplete material Stubs Topology http://www.artofproblemsolving.com/Wiki/index.php/Algebraic_topology

AoPSWiki Looking for a challenging algebra text? Preparing for MATHCOUNTS or the AMC exams? Check out Art of Problem Solving's Introduction to Algebra by Richard Rusczyk. Page Discussion View source History Personal tools Log in / create account Navigation Main Page Community portal Current events Recent changes ... Donations Search Toolbox What links here Related changes Upload file Special pages ... Permanent link Algebraic topology From AoPSWiki Algebraic topology is the study of topology using methods from abstract algebra . In general, given a topological space , we can associate various algebraic objects, such as groups and rings Fundamental Groups Perhaps the simplest object of study in algebraic topology is the fundamental group . Let be a path-connected topological space, and let be any point. Now consider all possible "loops" on

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