Algebraic L-theory and Topological Manifolds
By (author) A. A. Ranicki
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Algebraic L-theory and Topological Manifolds by A. A. Ranicki
Book DescriptionThis book presents a definitive account of the applications of the algebraic L-theory to the surgery classification of topological manifolds. The central result is the identification of a manifold structure in the homotopy type of a Poincare 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 Poincare 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. The book is designed as an introduction to the subject, accessible to graduate students in topology; no previous acquaintance with surgery theory is assumed, and every algebraic concept is justified by its occurrence in topology.
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Book DetailsISBN: 9780521055215
(228mm x 152mm x 21mm)
Imprint: Cambridge University Press
Publisher: Cambridge University Press
Publish Date: 21-Jan-2008
Country of Publication: United Kingdom
Books By Author A. A. Ranicki
Algebraic L-Theory and Topological Manifolds, Hardback (December 1992)» View all books by A. A. Ranicki
This book explains the applications of quadratic forms to the classification of topological manifolds, in a unified algebraic framework.
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