Algebraic Topology from a Homotopical Viewpoint [Paperback]

The authors present introductory material in algebraic topology from a novel point of view in using a homotopy-theoretic approach. This carefully written book can be read by any student who knows some topology, providing a useful method to quickly learn this novel homotopy-theoretic point of view of algebraic topology.

* Introduction * Basic Concepts and Notation * Function Spaces * Connectedness and Algebraic Invariants * Homotopy Groups * Homotopy Extentsion and Lifting Properties * CW-Complexes Homology * Homotopy Properties of CW-Complexes * Cohomology Groups and Related Topics * Vector Bundles * K-Theory * Adams Operations and Applications * Relations Between Cohomology and Vector Bundles * Cohomology Theories and Brown Representability * Appendix A: Proof of the Dold-Thom Theorem * Appendix B: Proof of the Bott Periodicity Theorem * References * Index * Glossary *

From the reviews:

This is a basic course on algebraic topology and & it is excellently written and composed and can be strongly recommended to anybody wishing to learn the field. The reader can find many examples, calculations, and also a number of exercises. & The book has two appendices, & references consisting of 83 items and a long list of symbols. There are many remarks and comments making the orientation of the reader in the field of algebraic topology easier & . (EMS, June, 2004)

The modus operandi of algebraic topology is to associate algebraic invariants, such as groups or rings, to a topological space in such a way that equivalent spaces exhibit isomorphic invariants; here, equivalent may be chosen to fit the geometry of the problem. In this book, equivalent means homotopy equivalent & . For its clarity and directness, a welcome addition to advanced mathematics collections. Upper-division undergraduates through faculty. (J. McCleary, CHOICE, December, 2002)

The purpose of this book is to introl*