Spaces of PL manifolds and categories of simple maps
Author(s)
Bibliographic Information
Spaces of PL manifolds and categories of simple maps
(Annals of mathematics studies, no. 186)
Princeton University Press, 2013
- : pbk
Available at 38 libraries
  Aomori
  Iwate
  Miyagi
  Akita
  Yamagata
  Fukushima
  Ibaraki
  Tochigi
  Gunma
  Saitama
  Chiba
  Tokyo
  Kanagawa
  Niigata
  Toyama
  Ishikawa
  Fukui
  Yamanashi
  Nagano
  Gifu
  Shizuoka
  Aichi
  Mie
  Shiga
  Kyoto
  Osaka
  Hyogo
  Nara
  Wakayama
  Tottori
  Shimane
  Okayama
  Hiroshima
  Yamaguchi
  Tokushima
  Kagawa
  Ehime
  Kochi
  Fukuoka
  Saga
  Nagasaki
  Kumamoto
  Oita
  Miyazaki
  Kagoshima
  Okinawa
  Korea
  China
  Thailand
  United Kingdom
  Germany
  Switzerland
  France
  Belgium
  Netherlands
  Sweden
  Norway
  United States of America
-
Library, Research Institute for Mathematical Sciences, Kyoto University数研
WAL||60||1200026165643
Note
Includes bibliographical references (p. [175]-178) and index
Description and Table of Contents
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.
Table of Contents
Introduction 1 1.The stable parametrized h-cobordism theorem 7 1.1. The manifold part 7 1.2. The non-manifold part 13 1.3. Algebraic K-theory of spaces 15 1.4. Relation to other literature 20 2.On simple maps 29 2.1. Simple maps of simplicial sets 29 2.2. Normal subdivision of simplicial sets 34 2.3. Geometric realization and subdivision 42 2.4. The reduced mapping cylinder 56 2.5. Making simplicial sets non-singular 68 2.6. The approximate lifting property 74 2.7. Subdivision of simplicial sets over DELTAq 83 3.The non-manifold part 99 3.1. Categories of simple maps 99 3.2. Filling horns 108 3.3. Some homotopy fiber sequences 119 3.4. Polyhedral realization 126 3.5. Turning Serre fibrations into bundles 131 3.6. Quillen's Theorems A and B 134 4.The manifold part 139 4.1. Spaces of PL manifolds 139 4.2. Spaces of thickenings 150 4.3. Straightening the thickenings 155 Bibliography 175 Symbols 179 Index 181
by "Nielsen BookData"