Homotopy type

Characteristic cohomology classes, defined in modulo 2 coefficients by Stiefel [26] and Whitney [28] and with integral coefficients by Pontrjagin [24], make up the primary source of first-order invariants of smooth manifolds. When their utility was first recognized, it became an obvious goal to study the ways in which they admitted extensions to other categories, such as the categories of topological or PL manifolds; perhaps a clean description of characteristic classes for simplicial complexes could even give useful computational techniques.

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This book grew out of courses which I taught at Cornell University and the University of Warwick during 1969 and 1970. I wrote it because of a strong belief that there should be readily available a semi-historical and geometrically motivated exposition of J. H. C. Whitehead's beautiful theory of simple-homotopy types; that the best way to understand this theory is to know how and why it was built.

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Allen Hatcher Copyright c 2000 by Allen Hatcher Paper or electronic copies for noncommercial use may be made freely without explicit permission from the author. All other rights reserved. .Table of Contents Chapter 0. Some Underlying Geometric Notions Homotopy and Homotopy Type 1. Cell Complexes 5. . . . . . 1 Operations on Spaces 8. Two Criteria for Homotopy Equivalence 11. The Homotopy Extension Property 14. Chapter 1. The Fundamental Group 1. Basic Constructions . . . . . . . . . . . . . 21 25 . . . . . . . . . . . . . . . . . . . . . ....

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