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On signatures associated with ramified coverings and embedding problems

J. WoodEmery Thomas — 1973

Annales de l'institut Fourier

Given a cohomology class ξ H 2 ( M ; Z ) there is a smooth submanifold K M Poincaré dual to ξ . A special class of such embeddings is characterized by topological properties which hold for nonsingular algebraic hypersurfaces in C P n . This note summarizes some results on the question: how does the divisibility of ξ restrict the dual submanifolds K in this class ? A formula for signatures associated with a d -fold ramified cover of M branched along K is given and a proof is included in case d = 2 .

Operator Segal algebras in Fourier algebras

Brian E. ForrestNico SpronkPeter J. Wood — 2007

Studia Mathematica

Let G be a locally compact group, A(G) its Fourier algebra and L¹(G) the space of Haar integrable functions on G. We study the Segal algebra S¹A(G) = A(G) ∩ L¹(G) in A(G). It admits an operator space structure which makes it a completely contractive Banach algebra. We compute the dual space of S¹A(G). We use it to show that the restriction operator u u | H : S ¹ A ( G ) A ( H ) , for some non-open closed subgroups H, is a surjective complete quotient map. We also show that if N is a non-compact closed subgroup, then the averaging...

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