Spaces of PL Manifolds and Categories of Simple Maps (AM-186) PDF
by Friedhelm Waldhausen, Bjorn Jahren, John Rognes
Part of the Annals of Mathematics Studies series
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 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.
Information
-
Download - Immediately Available
- Format:PDF
- Pages:192 pages
- Publisher:Princeton University Press
- Publication Date:21/04/2013
- Category:
- ISBN:9781400846528
Other Formats
- Hardback from £172.35
- Paperback / softback from £66.55
Information
-
Download - Immediately Available
- Format:PDF
- Pages:192 pages
- Publisher:Princeton University Press
- Publication Date:21/04/2013
- Category:
- ISBN:9781400846528
