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Spaces of PL Manifolds and Categories of Simple Maps (AM-186) - Princeton Scholarship Online
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Spaces of PL Manifolds and Categories of Simple Maps (AM-186)

Friedhelm Waldhausen, Bjørn Jahren, and John Rognes

Abstract

Since its introduction by the author 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 the author'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 ha ... More

Keywords: algebraic K-theory, space, PL manifold, h-cobordism theorem, homotopy equivalence, simple map, triangulation, desingularization

Bibliographic Information

Print publication date: 2013 Print ISBN-13: 9780691157757
Published to Princeton Scholarship Online: October 2017 DOI:10.23943/princeton/9780691157757.001.0001

Authors

Affiliations are at time of print publication.

Friedhelm Waldhausen, author
Universitat Bielefeld

Bjørn Jahren, author
University of Oslo

John Rognes, author
University of Oslo