Spaces of PL Manifolds and Categories of Simple Maps (AM-186) / Annals of Mathematics Studies Bd.186 (PDF)
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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.
- Autoren: Friedhelm Waldhausen , Bjørn Jahren , John Rognes
- 2013, 192 Seiten, Englisch
- Verlag: Bonnier Books UK
- ISBN-10: 1400846528
- ISBN-13: 9781400846528
- Erscheinungsdatum: 21.04.2013
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- Dateiformat: PDF
- Größe: 1.58 MB
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