Algebraic L-theory and Topological Manifolds

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Hardcover | 8 February 1993

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Hardcover
372 Pages

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22.86 x 15.24 x 2.54

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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 Poincar© 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 Poincar© 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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Non-Fiction Mathematics Topology Algebraic Topology Geometry Applied Mathematics

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Published: 20th March 2008

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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.

Algebraic L-theory and Topological Manifolds

At a Glance

Hardcover

Industry Reviews

Shipping

How to return your order

Defective items

You Can Find This Book In

Other Editions and Formats

Paperback

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