Overview
"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."
Full Product Details
Author: Friedhelm Waldhausen ,
Bjørn Jahren ,
John Rognes
Publisher: Princeton University Press
Imprint: Princeton University Press
Volume: 210
Weight: 0.397kg
ISBN: 9780691157757
ISBN 10: 0691157758
Pages: 192
Publication Date: 28 April 2013
Audience:
College/higher education
,
Professional and scholarly
,
Tertiary & Higher Education
,
Professional & Vocational
Format: Hardback
Publisher's Status: Active
Availability: Temporarily unavailable
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Language: English
Reviews
It is a welcome event, after 35 years, to have available a complete proof of Waldhausen's program. --Bruce Hughes, Zentralblatt MATH The book has been written with enormous patience but it is not for impatient readers. For me, appreciation came gradually with meditations on the vast historical context of the book and the fascinating pitfalls of combinatorial topology. --Michael Weiss, Jahresber
The book has been written with enormous patience but it is not for impatient readers. For me, appreciation came gradually with meditations on the vast historical context of the book and the fascinating pitfalls of combinatorial topology. --Michael Weiss, Jahresber It is a welcome event, after 35 years, to have available a complete proof of Waldhausen's program. --Bruce Hughes, Zentralblatt MATH
The book has been written with enormous patience but it is not for impatient readers. For me, appreciation came gradually with meditations on the vast historical context of the book and the fascinating pitfalls of combinatorial topology. --Michael Weiss, Jahresber
Author Information
Friedhelm Waldhausen is professor emeritus of mathematics at Bielefeld University. Bjrn Jahren is professor of mathematics at the University of Oslo. John Rognes is professor of mathematics at the University of Oslo.
