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  • Open Daily: 10am - 10pm
    Alley-side Pickup: 10am - 7pm

    3038 Hennepin Ave Minneapolis, MN
    612-822-4611

Open Daily: 10am - 10pm | Alley-side Pickup: 10am - 7pm
3038 Hennepin Ave Minneapolis, MN
612-822-4611
Spaces of PL Manifolds and Categories of Simple Maps (Am-186)

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

Jahren, Bjørn
Rognes, John
Waldhausen, Friedhelm

Paperback

Series: Annals of Mathematics Studies, Book 186

General Mathematics

ISBN10: 0691157766
ISBN13: 9780691157764
Publisher: Princeton Univ Pr
Published: Apr 28 2013
Pages: 192
Weight: 0.60
Height: 0.60 Width: 6.10 Depth: 9.10
Language: English

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.

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