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The Penrose Transform for Compactly Supported Cohomology
Author(s) -
Bailey Toby N.,
David Liana
Publication year - 2002
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/s0024610702003307
Subject(s) - mathematics , vector bundle , pure mathematics , cohomology , holomorphic function , group (periodic table) , kernel (algebra) , differential operator , operator (biology) , equivariant cohomology , differential form , complex manifold , algebra over a field , physics , biochemistry , chemistry , repressor , quantum mechanics , transcription factor , gene
Let the manifold X parametrise a family of compact complex submanifolds of the complex (or CR) manifold Z . Under mild conditions the Penrose transform typically provides isomorphisms between a cohomology group of a holomorphic vector bundle V → Z and the kernel of a differential operator between sections of vector bundles over X . When the spaces in question are homogeneous for a group G the Penrose transform provides an intertwining operator between representations. The paper develops a Penrose transform for compactly supported cohomology on Z . It provides a number of examples where a compactly supported cohomology group is shown to be isomorphic to the cokernel of a differential operator between compactly supported sections of vector bundles over X . It considers also how the Serre duality pairing carries through the transform.