Cellular Structures in Topology

Rudolf Fritsch; Renzo Piccinini

doi:10.1017/CBO9780511983948

This book describes the construction and the properties of CW-complexes. These spaces are important because firstly they are the correct framework for homotopy theory, and secondly most spaces that arise in pure mathematics are of this type. The authors discuss the foundations and also developments, for example, the theory of finite CW-complexes, CW-complexes in relation to the theory of fibrations, and Milnor's work on spaces of the type of CW-complexes. They establish very clearly the relationship between CW-complexes and the theory of simplicial complexes, which is developed in great detail. Exercises are provided throughout the book; some are straightforward, others extend the text in a non-trivial way. For the latter; further reference is given for their solution. Each chapter ends with a section sketching the historical development. An appendix gives basic results from topology, homology and homotopy theory. These features will aid graduate students, who can use the work as a course text. As a contemporary reference work it will be essential reading for the more specialized workers in algebraic topology and homotopy theory.

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Cellular Structures in Topology

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Contents

Frontmatter
pp i-vi

Contents
pp vii-viii

Preface
pp ix-xii

1 - The fundamental properties of CW-complexes
pp 1-55

2 - Categories of CW-complexes
pp 56-88

3 - Combinatorial complexes
pp 89-131

4 - Simplicial sets
pp 132-222

5 - Spaces of the type of CW-complexes
pp 223-240

Appendix
pp 241-305

Bibliography
pp 306-312

List of symbols
pp 313-320

Index
pp 321-326

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