Algebraic L-theory and topological manifolds
A. A. Ranicki
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.
Կատեգորիաներ:
Տարի:
2008
Հրատարակում:
1
Հրատարակչություն:
Cambridge University Press
Լեզու:
english
Էջեր:
189
ISBN 10:
0521055210
ISBN 13:
9780521055215
Սերիաներ:
Cambridge Tracts in Mathematics
Ֆայլ:
DJVU, 2.53 MB
IPFS:
,
english, 2008