UID:
almafu_9959241198402883
Format:
1 online resource (193 p.)
Edition:
Course Book
ISBN:
1-4008-4652-8
,
1-299-05144-8
Series Statement:
Annals of Mathematics Studies ; 210
Content:
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.
Note:
Description based upon print version of record.
,
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
,
Issued also in print.
,
English
Additional Edition:
ISBN 0-691-15775-8
Additional Edition:
ISBN 0-691-15776-6
Language:
English
Subjects:
Mathematics
DOI:
10.1515/9781400846528