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Algebraic topology

Author: Allen Hatcher
Publisher: Cambridge, UK ; New York : Cambridge University Press, [2001], ©2002.
Edition/Format:   Print book : EnglishView all editions and formats
Database:WorldCat
Summary:
'In most mathematics departments at major universities one of the three or four basic first-year graduate courses is in the subject of algebraic topology. This introductory textbook in algebraic topology is suitable for use in a course or for self-study, featuring broad coverage of the subject and a readable exposition, with many examples and exercises. The four main chapters present the basic material of the  Read more...
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Genre/Form: Lehrbuch
Document Type: Book
All Authors / Contributors: Allen Hatcher
ISBN: 052179160X 9780521791601 0521795400 9780521795401
OCLC Number: 52264002
Description: xii, 544 pages : illustrations ; 26 cm
Contents: Some Underlying Geometric Notions --
Homotopy and Homotopy Type --
Cell Complexes --
Operations on Spaces --
Two Criteria for Homotopy Equivalence --
The Homotopy Extension Property --
The Fundamental Group --
Basic Constructions --
Paths and Homotopy --
The Fundamental Group of the Circle --
Induced Homomorphisms --
Van Kampen's Theorem --
Free Products of Groups --
The van Kampen Theorem --
Applications to Cell Complexes --
Covering Spaces --
Lifting Properties --
The Classification of Covering Spaces --
Deck Transformations and Group Actions --
Graphs and Free Groups --
K(G,1) Spaces and Graphs of Groups --
Homology --
Simplicial and Singular Homology --
[Delta]-Complexes --
Simplicial Homology --
Singular Homology --
Homotopy Invariance --
Exact Sequences and Excision --
The Equivalence of Simplicial and Singular Homology --
Computations and Applications --
Degree --
Cellular Homology --
Mayer-Vietoris Sequences --
Homology with Coefficients --
The Formal Viewpoint --
Axioms for Homology --
Categories and Functors --
Homology and Fundamental Group --
Classical Applications --
Simplicial Approximation --
Cohomology --
Cohomology Groups --
The Universal Coefficient Theorem --
Cohomology of Spaces --
Cup Product --
The Cohomology Ring --
A Kunneth Formula --
Spaces with Polynomial Cohomology --
Poincare Duality --
Orientations and Homology --
The Duality Theorem --
Connection with Cup Product --
Other Forms of Duality --
Universal Coefficients for Homology --
The General Kunneth Formula.
Responsibility: Allen Hatcher.

Abstract:

An introductory textbook suitable for use in a course or for self-study, featuring broad coverage of the subject and a readable exposition, with many examples and exercises.  Read more...

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'... this is a marvellous tome, which is indeed a delight to read. This book is destined to become very popular amongst students and teachers alike.' Bulletin of the Belgian Mathematical Society '... Read more...

 
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