UID:
edocfu_9958352865102883
Format:
1 online resource(192p.) :
,
illustrations.
Edition:
Electronic reproduction. Princeton, N.J. : Princeton University Press, 2013. Mode of access: World Wide Web.
Edition:
System requirements: Web browser.
Edition:
Access may be restricted to users at subscribing institutions.
ISBN:
9781400846528
Series Statement:
Annals of Mathematics Studies, 186
Content:
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.
Note:
Frontmatter --
,
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.
,
In English.
Language:
English
DOI:
10.1515/9781400846528
URL:
https://doi.org/10.1515/9781400846528
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