Algebraic L-theory and Topological Manifolds (Cambridge Tracts in Mathematics)

by A. A. Ranicki

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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 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. 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.
  • ISBN13 9780521420242
  • Publish Date 10 December 1992
  • Publish Status Active
  • Out of Print 6 June 2022
  • Publish Country GB
  • Imprint Cambridge University Press
  • Format Hardcover
  • Pages 372
  • Language English