Algebraic L-theory And Topological Manifolds (cambridge Tracts In Mathematics)
by A. A. Ranicki /
2008 / English / PDF
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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.
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.
