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Fundamentals of Algebraic Topology

This rapid and concise presentation of the essential ideas and results of algebraic topology follows the axiomatic foundations pioneered by Eilenberg and Steenrod. The approach of the book is pragmatic: while most proofs are given, those that are particularly long or technical are omitted, and resul...

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Main Author: Weintraub, Steven H. (Author, http://id.loc.gov/vocabulary/relators/aut)
Corporate Author: SpringerLink (Online service)
Language:English
Published: New York, NY : Springer New York : Imprint: Springer, 2014.
Edition:1st ed. 2014.
Series:Graduate Texts in Mathematics, 270
Subjects:
Algebraic topology.
Manifolds (Mathematics).
Complex manifolds.
Category theory (Mathematics).
Homological algebra.
Algebraic Topology.
Manifolds and Cell Complexes (incl. Diff.Topology).
Category Theory, Homological Algebra.
Online Access:https://doi.org/10.1007/978-1-4939-1844-7
Table of Contents:
  • Preface
  • 1. The Basics
  • 2. The Fundamental Group
  • 3. Generalized Homology Theory
  • 4. Ordinary Homology Theory
  • 5. Singular Homology Theory
  • 6. Manifolds
  • 7. Homotopy Theory
  • 8. Homotopy Theory
  • A. Elementary Homological Algebra
  • B. Bilinear Forms.- C. Categories and Functors
  • Bibliography
  • Index.

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