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Algebraic L theory and Topological Manifolds Cambridge Tracts in Mathematics Series Number 102

by [Ranicki, A. A.]

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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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Product Details

  • Cambridge University Pres Brand
  • Jan 29, 1993 Pub Date:
  • 9780521420242 ISBN-13:
  • 0521420245 ISBN-10:
  • 372.0 pages Hardcover
  • English Language
  • 9.5 in * 0.75 in * 6.5 in Dimensions:
  • 1 lb Weight: