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Spaces of PL Manifolds and Categories of Simple Maps (Paperback)

Friedhelm Waldhausen, Björn Jahren, John Rognes

Edité par Princeton University Press, United States, 2013
ISBN 10: 0691157766 / ISBN 13: 9780691157764
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Titre : Spaces of PL Manifolds and Categories of ...

Éditeur : Princeton University Press, United States

Date d'édition : 2013

Reliure : Paperback

Etat du livre : New

Description :

Language: English . Brand New Book. 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. N° de réf. du libraire AAH9780691157764

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