Description
Book SynopsisSince 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 Waldhau
Trade Review"The book has been written with enormous patience but it is not for impatient readers. For me, appreciation came gradually with meditations on the vast historical context of the book and the fascinating pitfalls of combinatorial topology."--Michael Weiss, Jahresber "It is a welcome event, after 35 years, to have available a complete proof of Waldhausen's program."--Bruce Hughes, Zentralblatt MATH
Table of ContentsIntroduction 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
