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Algebraic L-theory and Topological Manifolds : Cambridge Tracts in Mathematics - A. A. Ranicki

Algebraic L-theory and Topological Manifolds

Cambridge Tracts in Mathematics

Hardcover

Published: 4th February 2003
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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 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.

"...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

Introduction
Algebra
Algebraic Poincare complexes
Algebraic normal complexes
Algebraic normal categories
Categories over complexes
Duality
Simply-connected assembly
Derived products and Hom
Local Poincare duality
Universal assembly
The algebraic p-p theorem
?-sets
Generalised 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 Poincare complexes
The simply-connected case
Transfer
Finite fundamental group
Splitting
Higher signatures
Periodicity
Surgery with coefficients
Appendices
References
Index
Table of Contents provided by Publisher. All Rights Reserved.

ISBN: 9780521420242
ISBN-10: 0521420245
Series: Cambridge Tracts in Mathematics
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 372
Published: 4th February 2003
Publisher: Cambridge University Press
Country of Publication: GB
Dimensions (cm): 22.8 x 15.2  x 2.5
Weight (kg): 0.75