SPACES OF PL MANIFOLDS AND CATEGORIES OF SIMPLE MAPS (AM-186)


Ebook SPACES OF PL MANIFOLDS AND CATEGORIES OF SIMPLE MAPS (AM-186) by FRIEDHELM WALDHAUSEN, BJØRN JAHREN, JOHN ROGNES Book Title: SPACES OF PL MANIFOLDS AND CATEGORIES OF SIMPLE MAPS (AM-186)
The size of the: 4 MB
Edition: Otava
Date of issue: 2016
ISBN: No data
ISBN 13: No data
The author of the book:FRIEDHELM WALDHAUSEN, BJØRN JAHREN, JOHN ROGNES
Language: English
Format files: PDF

Product Description

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 Waldhausens 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.

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