Friedhelm Waldhausen

(Author)

Spaces of PL Manifolds and Categories of Simple Maps (Am-186)Hardcover, 28 April 2013

Spaces of PL Manifolds and Categories of Simple Maps (Am-186)
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Part of Series
Annals of Mathematics Studies
Part of Series
Annals of Mathematics Studies (Hardcover)
Part of Series
Annals of Mathematics Studies, 186
Print Length
192 pages
Language
English
Publisher
Princeton University Press
Date Published
28 Apr 2013
ISBN-10
0691157758
ISBN-13
9780691157757

Description

Since its introduction by Friedhelm Waldhausen in the 1970s, 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.

Product Details

Authors:
Friedhelm WaldhausenBjørn JahrenJohn Rognes
Book Format:
Hardcover
Country of Origin:
US
Date Published:
28 April 2013
Genre:
Science/Technology Aspects
ISBN-10:
0691157758
ISBN-13:
9780691157757
Language:
English
Location:
Princeton
Pages:
192

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