Algebraic L-Theory and Topological Manifolds

By: A. A. Ranicki

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Paperback | 20 March 2008

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372 Pages

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22.86 x 15.24 x 2.11

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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.

Industry 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

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Introduction
Summary
Algebra
Algebraic PoincarF complexes
Algebraic normal complexes
Algebraic bordism categories
Categories over complexes
Duality
Simply connected assembly
Derived product and Hom
Local PoincarF duality
Universal assembly
The algebraic - theorem
-sets
Generalized homology theory
Algebraic L-spectra
The algebraic surgery exact sequence
Connective L-theory
Topology
The L-theory orientation of topology
The total surgery obstruction
The structure set
Geometric PoincarF complexes
The simply connected case
Transfer
Finite fundamental group
Splitting
Higher signatures
The 4-periodic theory
Surgery with coefficients
Appendices
Bibliography
Index
Table of Contents provided by Publisher. All Rights Reserved.

Algebraic L-Theory and Topological Manifolds

At a Glance

Paperback

Industry Reviews

Shipping

How to return your order

Defective items

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