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Algebraic Topology:     more books (100)

A User's Guide to Algebraic Topology (Mathematics and Its Applications) by C.T. Dodson, P.E. Parker, et all 1997-01-31 Algebraic Topology (EMS Textbooks in Mathematics) by Tammo Tom Dieck, 2008-09-15 Differential Algebraic Topology (Graduate Studies in Mathematics) by Matthias Kreck, 2010-05-04 Essential Topology (Springer Undergraduate Mathematics Series) by Martin D. Crossley, 2005-07-01 Algebraic Topology: A First Course (Mathematics Lecture Note Series) by Marvin J. Greenberg, John R. Harper, 1981-01-22 Algebraic Topology via Differential Geometry (London Mathematical Society Lecture Note Series) by M. Karoubi, C. Leruste, 1988-01-29 Lectures on algebraic topology (Mathematics lecture note series) by Marvin J Greenberg, 1967 Introduction to Differential and Algebraic Topology (Texts in the Mathematical Sciences) by Yu.G. Borisovich, N.M. Bliznyakov, et all 2010-11-02 Algebraic Topology by Robert M. Switzer, 2002-02-26 Quadratic Forms with Applications to Algebraic Geometry and Topology (London Mathematical Society Lecture Note Series) by Albrecht Pfister, 1995-10-27 Foundations of Algebraic Topology (Mathematics Series) by Samuel Eilenberg, Norman E. Steenrod, 1952-12 Homology Theory: An Introduction to Algebraic Topology (Graduate Texts in Mathematics) (v. 145) by James W. Vick, 1994-01-07 Hodge Theory and Complex Algebraic Geometry I: Volume 1 (Cambridge Studies in Advanced Mathematics) (v. 1) by Claire Voisin, 2008-02-04 A Combinatorial Introduction to Topology by Michael Henle, 1994-03-14

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    Extractions: Jump to: navigation search Hatcher, A., Algebraic Topology Cambridge Univ. Press (2002) ISBN 0-521-79540-0 . Detailed discussion of homology theories for simplicial complexes and manifolds, singular homology, etc. Retrieved from " http://www.mathematics.thetangentbundle.net/wiki/Algebraic_topology Views Personal tools Navigation Search Toolbox What links here Related changes Upload file Special pages ... Permanent link This page was last modified 18:27, 17 October 2007. This page has been accessed 91 times. Content is available under GNU Free Documentation License About Mathematics

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    Extractions: Home 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 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 that start and end at , i.e. all continuous functions with . Call this collection . Now define an equivalence relation on by saying that if there is a continuous function with , and . We call a homotopy . Now define . That is, we equate any two elements of which are equivalent under Unsurprisingly, the fundamental group is a group. The identity is the equivalence class containing the map given by for all . The inverse of a map is the map given by . We can compose maps as follows: One can check that this is indeed well-defined Note that the fundamental group is not in general abelian . For example, the fundamental group of a figure eight is the

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    Extractions: Categories Topology Algebraic topology Abstract algebra ... Wikipedia Article ज्ञानकोश: - The Indological Knowledgebase Algebraic topology is a branch of mathematics in which tools from abstract algebra are used to study topological spaces Contents showTocToggle("show","hide") 1 The method of algebraic invariants edit 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 basic method now applied in algebraic topology is to investigate spaces via algebraic invariants: for example by mapping them to groups , which have a great deal of manageable structure, in a way that respects the relation of homeomorphism of spaces. Two major ways in which this can be done are through fundamental groups , or more general 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

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    Extractions: Astronomy Biology Chemistry ... Discuss Article 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 or classify them. An older name for the subject was combinatorial topology , implying an emphasis on how a space X was contructed from simpler ones. The basic method now applied in algebraic topology is to investigate spaces via algebraic invariants: for example by mapping them to groups , which have a great deal of manageable structure, in a way that respects the relation of homeomorphism of spaces. Two major ways in which this can be done are through fundamental groups, or more general 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 nonabelian and can be difficult to work with. The fundamental group of a (finite)

50. Wikipedia Algebraic Topology
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    Extractions: 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 or classify them. An older name for the subject was combinatorial topology , implying an emphasis on how a space X was contructed from simpler ones. The basic method now applied in algebraic topology is to investigate spaces via algebraic invariants: for example by mapping them to groups , which have a great deal of manageable structure, in a way that respects the relation of homeomorphism of spaces. Two major ways in which this can be done are through fundamental groups, or more general 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 nonabelian and can be difficult to work with. The fundamental group of a (finite)

51. Algebraic Topology - Wikipedia, The Free Encyclopedia - Darmowe.org.pl
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    Extractions: 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 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

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56. ø Algebraic Topology Data ø
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    Extractions: www.aadet.com Site Search: Years history Algebraic topology is a branch of mathematics in which tools from abstract algebra are used to study topological space s. 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 group s, 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

57. Algebraic Topology - Wikipedia, The Free Encyclopedia
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    Extractions: edit 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 basic method now applied in algebraic topology is to investigate spaces via algebraic invariants: for example by mapping them to groups , which have a great deal of manageable structure, in a way that respects the relation of homeomorphism of spaces. 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 nonabelian and can be difficult to work with. The fundamental group of a (finite)

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    Extractions: Search the web: search the entire directory search this category only Top Science Math Topology See also: Science: Math: Algebra Science: Math: Algebra: Category Theory Allen Hatcher's Homepage - Links to online texts and papers (published and unpublished) on Algebraic Topology, K-Theory, and 3-Manifolds.

60. Algebraic Topology Books, Book Price Comparison At 130 Bookstores
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