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Algebraic L-theory and Topological Manifolds (Cambridge Tracts in Mathematics, Series Number 102)

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Algebraic L-theory and Topological Manifolds (Cambridge Tracts in Mathematics, Series Number 102) image
ISBN-10:

0521055210

ISBN-13:

9780521055215

Author(s): Ranicki, A.A.
Edition: 1
Released: Jan 21, 2008
Publisher: Cambridge University Press
Format: Paperback, 372 pages
Related ISBN: 9780521420242
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Description:

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 Poincaré 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 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 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.

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