Algebraic L-theory and Topological Manifolds
Algebraic L-theory and Topological Manifolds This book presents a definitive account of the applications of the algebraic L-theory to the surgery classification of topological manifolds. The…
Specifikacia Algebraic L-theory and Topological Manifolds
Algebraic L-theory and Topological Manifolds
This book presents a definitive account of the applications of the algebraic L-theory to the surgery classification of topological manifolds. The difference between the homotopy types of manifolds and Poincaré 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 central result is the identification of a manifold structure in the homotopy type of a Poincaré duality space with a local quadratic structure in the chain homotopy type of the universal cover.
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. 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.