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The Topology of CW Complexes

  • Albert T. Lundell
  • Stephen Weingram

Part of the The University Series in Higher Mathematics book series (USHM)

Table of contents

  1. Front Matter
    Pages i-viii
  2. Albert T. Lundell, Stephen Weingram
    Pages 1-5
  3. Albert T. Lundell, Stephen Weingram
    Pages 6-40
  4. Albert T. Lundell, Stephen Weingram
    Pages 41-76
  5. Albert T. Lundell, Stephen Weingram
    Pages 77-115
  6. Albert T. Lundell, Stephen Weingram
    Pages 116-142
  7. Albert T. Lundell, Stephen Weingram
    Pages 143-200
  8. Back Matter
    Pages 201-216

About this book

Introduction

Most texts on algebraic topology emphasize homological algebra, with topological considerations limited to a few propositions about the geometry of simplicial complexes. There is much to be gained however, by using the more sophisticated concept of cell (CW) complex. Even for simple computations, this concept ordinarily allows us to bypass much tedious algebra and often gives geometric insight into the homology and homotopy theory of a space. For example, the easiest way to calculate and interpret the homology of Cpn, complex projective n-space, is by means of a cellular decomposition with only n+ 1 cells. Also, by a suitable construction we can "realize" the sin­ gular complex of a space as a CW complex and perhaps thus give a more geometric basis for some arguments involving singular homology theory for general spaces and a more concrete basis for singular ho­ motopy type. As a fInal example, if we start with the category of sim­ plicial complexes and maps, common topological constructions such as the formation of product spaces, identifIcation spaces, and adjunction spaces lead us often into the category of CW complexes. These topics, among others, are usually not treated thoroughly in a standard text, and the interested student must fInd them scattered through the literature. This book is a study of CW complexes. It is intended to supplement and be used concurrently with a standard text on algebraic topology.

Keywords

algebra geometry homology homotopy topology

Authors and affiliations

  • Albert T. Lundell
    • 1
  • Stephen Weingram
    • 2
  1. 1.University of ColoradoBoulderUSA
  2. 2.Purdue UniversityLafayetteUSA

Bibliographic information