Algebraic L-Theory and Topological Manifolds (Paperback) (ISBN-13: 9780521055215)

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.

Author: A. A. Ranicki
ISBN-10: 0521055210
ISBN-13: 9780521055215
Publisher: Cambridge University Press
Language: English
Published: 01/21/2008
Pages: 372
Format: Paperback
Weight: 1.20lbs
Size: 9.00h x 6.00w x 0.83d