Spaces of PL manifolds and categories of simple maps / Friedhelm Waldhausen, Bjørn Jahren and John Rognes.

Format:

Book

Author/Creator:

Waldhausen, Friedhelm, 1938-

Contributor:

Jahren, Bjørn, 1945-

Rognes, John.

Series:

Annals of Mathematics Studies

Annals of mathematics studies ; no. 186

Annals of Mathematics Studies ; 210

Language:

English

Subjects (All):

Piecewise linear topology.

Mappings (Mathematics).

Physical Description:

1 online resource (193 p.)

Edition:

Course Book

Place of Publication:

Princeton : Princeton University Press, 2013.

Language Note:

English

Summary:

Since its introduction by Friedhelm Waldhausen in the 1970's, the algebraic K-theory of spaces has been recognized as the main tool for studying parametrized phenomena in the theory of manifolds. However, a full proof of the equivalence relating the two areas has not appeared until now. This book presents such a proof, essentially completing Waldhausen's program from more than thirty years ago. The main result is a stable parametrized h-cobordism theorem, derived from a homotopy equivalence between a space of PL h-cobordisms on a space X and the classifying space of a category of simple maps of spaces having X as deformation retract. The smooth and topological results then follow by smoothing and triangulation theory. The proof has two main parts. The essence of the first part is a "desingularization," improving arbitrary finite simplicial sets to polyhedra. The second part compares polyhedra with PL manifolds by a thickening procedure. Many of the techniques and results developed should be useful in other connections.

Contents:

Front matter

Contents

Introduction

1. The stable parametrized h-cobordism theorem

2. On simple maps

3. The non-manifold part

4. The manifold part

Bibliography

Symbols

Index

Notes:

Description based upon print version of record.

Includes bibliographical references and index.

ISBN:

9781400846528

1400846528

9781299051447

1299051448

OCLC:

828077867