Spaces of PL Manifolds and Categories of Simple Maps (AM-186) /

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 pre...

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Bibliographic Details
Main Author: Waldhausen, Friedhelm, 1938-
Other Authors: Rognes, John, Jahren, Bjorn, 1945-
Format: Electronic eBook
Language:Inglés
Published: Princeton : Princeton University Press, 2013.
Series:Book collections on Project MUSE.
Subjects:
Piecewise linear topology.
Mappings (Mathematics)
MATHEMATICS > Transformations.
MATHEMATICS > Topology.
Applications (Mathematiques)
Topologie lineaire par morceaux.
Electronic books.
Online Access:Texto completo
Description
Summary: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.
Physical Description:1 online resource.
ISBN:9781400846528

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