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

Released on by Friedhelm Waldhausen
preview-18

  • Spaces of PL Manifolds and Categories of Simple Maps (AM-186) Book Detail

  • Author : Friedhelm Waldhausen
  • Release Date : 2013-04-21
  • Publisher : Princeton University Press
  • Genre : Mathematics
  • Pages : 193
  • ISBN 13 : 1400846528
  • File Size : 21,21 MB
DOWNLOAD BOOK

Spaces of PL Manifolds and Categories of Simple Maps (AM-186) by Friedhelm Waldhausen PDF Summary

Book 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.

Disclaimer: www.yourbookbest.com does not own Spaces of PL Manifolds and Categories of Simple Maps (AM-186) books pdf, neither created or scanned. We just provide the link that is already available on the internet, public domain and in Google Drive. If any way it violates the law or has any issues, then kindly mail us via contact us page to request the removal of the link.

Current Trends in Algebraic Topology

Current Trends in Algebraic Topology

File Size : 9,9 MB
Total View : 3724 Views
DOWNLOAD

Proceedings of a Conference held at the University of Western Ontario in 1981. More than one hundred papers were presented by researchers from a wide spectrum o