Spaces of PL Manifolds and Categories of Simple Maps (Annals of Mathematics Studies, 186)
Language: English
Published by Princeton University Press, 2013
- Softcover
- Used
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*Price Has BEEN REDUCED by 10% until Monday, Oct. 12 (SALE item)* 192 pp., paperback, very good. - If you are reading this, this item is actually (physically) in our stock and ready for shipment once ordered. We are not bookjackers. Buyer is responsible for any additional duties, taxes, or fees required by recipient's country.
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- Title
- Spaces of PL Manifolds and Categories of Simple Maps (Annals of Mathematics Studies, 186)
- Author
- Waldhausen, Friedhelm, Jahren, Bjà rn, Rognes, John
- Publisher
- Princeton University Press
- Publication year
- 2013
- Condition
- Very Good
- Binding
- Soft cover
- Language
- English
- ISBN 10
- 0691157766
- ISBN 13
- 9780691157764
- Series
- Book 40 of 202: Annals of Mathematics Studies
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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Zubal-Books, Since 1961
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