The Topological Classification of Stratified Spaces

The Topological Classification of Stratified Spaces

by Shmuel Weinberger
     
 

ISBN-10: 0226885674

ISBN-13: 9780226885674

Pub. Date: 01/28/1995

Publisher: University of Chicago Press

This book provides the theory for stratified spaces, along with important examples and applications, that is analogous to the surgery theory for manifolds. In the first expository account of this field, Weinberger provides topologists with a new way of looking at the classification theory of singular spaces with his original results.

Divided into three parts, the

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Overview

This book provides the theory for stratified spaces, along with important examples and applications, that is analogous to the surgery theory for manifolds. In the first expository account of this field, Weinberger provides topologists with a new way of looking at the classification theory of singular spaces with his original results.

Divided into three parts, the book begins with an overview of modern high-dimensional manifold theory. Rather than including complete proofs of all theorems, Weinberger demonstrates key constructions, gives convenient formulations, and shows the usefulness of the technology. Part II offers the parallel theory for stratified spaces. Here, the topological category is most completely developed using the methods of "controlled topology." Many examples illustrating the topological invariance and noninvariance of obstructions and characteristic classes are provided. Applications for embeddings and immersions of manifolds, for the geometry of group actions, for algebraic varieties, and for rigidity theorems are found in Part III.

This volume will be of interest to topologists, as well as mathematicians in other fields such as differential geometry, operator theory, and algebraic geometry.

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Product Details

ISBN-13:
9780226885674
Publisher:
University of Chicago Press
Publication date:
01/28/1995
Series:
Chicago Lectures in Mathematics
Edition description:
1
Pages:
283
Product dimensions:
6.00(w) x 9.00(h) x 0.80(d)

Table of Contents

Preface
0Introduction1
Pt. IThe Theory of Manifolds17
1Algebraic K-theory and topology19
2Surgery theory45
3Specification and functoriality70
4Applications86
Pt. IIThe General Theory of Stratified Spaces113
5Definitions and examples115
6Classification of stratified spaces126
7Transverse stratified classification139
8PT category143
9Controlled topology148
10Proof of main theorems in Top182
Pt. IIIApplications191
11Manifolds and embedding theory revisited193
12Supernormal spaces and varieties202
13Group actions217
14Rigidity conjectures241
Bibliography265
Index279

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