Overview
- Authors:
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Albert T. Lundell
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University of Colorado, Boulder, USA
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Stephen Weingram
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Purdue University, Lafayette, USA
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Table of contents (6 chapters)
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Front Matter
Pages i-viii
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- Albert T. Lundell, Stephen Weingram
Pages 1-5
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- Albert T. Lundell, Stephen Weingram
Pages 6-40
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- Albert T. Lundell, Stephen Weingram
Pages 41-76
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- Albert T. Lundell, Stephen Weingram
Pages 77-115
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- Albert T. Lundell, Stephen Weingram
Pages 116-142
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- Albert T. Lundell, Stephen Weingram
Pages 143-200
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Back Matter
Pages 201-216
About this book
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.
Authors and Affiliations
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University of Colorado, Boulder, USA
Albert T. Lundell
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Purdue University, Lafayette, USA
Stephen Weingram
