Spaces of PL Manifolds and Categories of Simple Maps AM 186 is popular PDF and ePub book, written by Friedhelm Waldhausen in 2013-04-21, it is a fantastic choice for those who relish reading online the Mathematics genre. Let's immerse ourselves in this engaging Mathematics book by exploring the summary and details provided below. Remember, Spaces of PL Manifolds and Categories of Simple Maps AM 186 can be Read Online from any device for your convenience.
Spaces of PL Manifolds and Categories of Simple Maps AM 186 Book PDF 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. 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.
Detail Book of Spaces of PL Manifolds and Categories of Simple Maps AM 186 PDF
- Author : Friedhelm Waldhausen
- Release : 21 April 2013
- Publisher : Princeton University Press
- ISBN : 9781400846528
- Genre : Mathematics
- Total Page : 193 pages
- Language : English
- PDF File Size : 13,5 Mb
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