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Verlag: Princeton University Press, 2013
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Zustand: New. Series: Annals of Mathematics Studies. Num Pages: 192 pages, 5 line illus. BIC Classification: PBKF; PBP. Category: (P) Professional & Vocational; (U) Tertiary Education (US: College). Dimension: 158 x 234 x 10. Weight in Grams: 280. . 2013. Paperback. . . . . Books ship from the US and Ireland.
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Taschenbuch. Zustand: Neu. Neuware - 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.