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THE PENROSE TRANSFORM FOR COMPACTLY SUPPORTED COHOMOLOGY

Published online by Cambridge University Press:  24 March 2003

TOBY N. BAILEY
Affiliation:
School of Mathematics, University of Edinburgh, Kings Buildings, Mayfield Road, Edinburgh EH9 3JZ tnb@maths.ed.ac.uklili@mail.dnttm.ro
LIANA DAVID
Affiliation:
School of Mathematics, University of Edinburgh, Kings Buildings, Mayfield Road, Edinburgh EH9 3JZ tnb@maths.ed.ac.uklili@mail.dnttm.ro
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Abstract

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 $V\longrightarrow Z$ 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.

Type
Notes and Papers
Copyright
The London Mathematical Society, 2002

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