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- W2022587622 abstract "In a previous paper we obtained an algebraic description of the transfer maps p∗:L n ( Z [π 1 (B)]→L n+d ( Z [π 1 (e)]) induced in the Wall surgery obstruction groups by a fibration with the fibre F a d -dimensional Poincaré complex. In this paper we define a Π 1 ( B )-equivariant symmetric signature σ∗(F, ω)ϵL d (π 1 (b), Z ) depending only on the fibre transport ω : Π 1 ( B )→[ F , F ], and prove that the composite p ∗ p∗:L n ( Z [π 1 (B)])→L n+d ( Z [π 1 (b)] is the evaluation σ∗(F, ω)⊗ ? of the product ⊗:L d (π 1 (B), Z ⊗L n ( Z [π 1 (B)])→L n+d ( Z [π 1 (B)]) . This is applied to prove vanishing results for the surgery transfer, such as p∗=0 if F = G is a compact connected d -dimensional Lie group which is not a torus, and is a G -principal bundle. An appendix relates this expression for p∗p ∗ to the twisted signature formula of Atiyah, Lusztig and Meyer." @default.
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- W2022587622 date "1992-08-01" @default.
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- W2022587622 title "Surgery obstructions of fibre bundles" @default.
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- W2022587622 doi "https://doi.org/10.1016/0022-4049(92)90003-x" @default.
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