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Algebraic L-theory and Topological Manifolds

1 / 1

Algebraic L-theory and Topological Manifolds

606 kr
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
  • Teknikk, Matematikk & Statistikk
  • Bok
  • Pocket
  • English
  • 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.
  • Sjanger
    Teknikk Matematikk & Statistikk
  • Formater
    Bok
  • EAN
    9780521055215
  • Publisher
    Cambridge University Press
  • Innbindning
    Pocket
  • Språk
    English
  • ISBN
    9780521055215
  • Læremiddel
    0
  • Serie
    Cambridge Tracts in Mathematics
  • Størrelse
    372
  • Forfatter
    A. A. Ranicki
0
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