This 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.

This book explains the applications of quadratic forms to the classification of topological manifolds, in a unified algebraic framework.
Reviews
"...develops lower K- and L-theory with a view to applications in topology....Apart from the obvious interest of this text both to topologists and to K-theorists, it also serves as an introduction to the field, since there is a comprehensive survey of previous results and applications." M.E. Keating, Bulletin of the London Mathematical Society



Book Information
ISBN 9780521055215
Author A. A. Ranicki
Format Paperback
Page Count 372
Imprint Cambridge University Press
Publisher Cambridge University Press
Weight(grams) 600g
Dimensions(mm) 228mm * 151mm * 20mm