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Algebraic L-Theory and Topological Manifolds
Contributor(s): Ranicki, A. A. (Author)

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 ISBN: 0521055210     ISBN-13: 9780521055215
Publisher: Cambridge University Press
OUR PRICE: $64.59  

Binding Type: Paperback - See All Available Formats & Editions
Published: January 2008
Qty:

Click for more in this series: Cambridge Tracts in Mathematics (Paperback)
Additional Information
BISAC Categories:
- Mathematics | Geometry - General
- Mathematics | Applied
- Mathematics | Topology - General
Dewey: 514.72
Series: Cambridge Tracts in Mathematics (Paperback)
Physical Information: 0.83" H x 6" W x 9" L (1.20 lbs) 372 pages
Features: Bibliography
 
Descriptions, Reviews, Etc.
Publisher Description:
This book presents the definitive account of the applications of this algebra to the surgery classification of topological manifolds. The central result is the identification of a manifold structure in the homotopy type of a Poincar duality space with a local quadratic structure in the chain homotopy type of the universal cover. The difference between the homotopy types of manifolds and Poincar duality spaces is identified with the fibre of the algebraic L-theory assembly map, which passes from local to global quadratic duality structures on chain complexes. The algebraic L-theory assembly map is used to give a purely algebraic formulation of the Novikov conjectures on the homotopy invariance of the higher signatures; any other formulation necessarily factors through this one.
 
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