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.
General
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