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- W1566877525 abstract "for any oriented covering X with group of covering translations π. If X is the universal cover, σ∗(f, b) is the surgery obstruction, and σ∗(f, b) = 0 if (and for n ≥ 5 only if) (f, b) is normally bordant to a homotopy equivalence. The n-dimensional quadratic L-group Ln(A) was expressed in Ranicki [4,6] as the cobordism group of n-dimensional quadratic Poincare complexes over A, which are chain complexes C of finitely generated free A-modules with an n-dimensional quadratic structure ψ inducing Poincare duality isomorphisms (1+T )ψ0 : Hn−∗(C) ∼= H∗(C). The symmetric L-groups L(A) (n ≥ 0) were introduced by Mishchenko [1] to describe the symmetric part of the surgery obstruction, and are not 4-periodic in general. The n-dimensional symmetric L-group L(A) is the cobordism group of n-dimensional symmetric Poincare complexes over A, which are chain complexes C of finitely generated free A-modules with an n-dimensional symmetric structure φ inducing Poincare duality isomorphisms φ0 : Hn−∗(C) ∼= H∗(C). A geometric Poincare complex X determines its symmetric signature (or “higher signature”)" @default.
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- W1566877525 date "1993-01-01" @default.
- W1566877525 modified "2023-09-23" @default.
- W1566877525 title "SYMMETRIC AND QUADRATIC COMPLEXES WITH GEOMETRIC CONTROL" @default.
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