Regularized cohomology of a non-compact asymptotically Kahler G-manifold

Details Regularized cohomology of a non-compact asymptotically Kahler G-manifold Regularized cohomology of a non-compact asymptotically Kahler G-manifold

2012-03-30

arxiv.org/abs/1203.6860v2

Mathematics

Differential Geometry

minor misprints are corrected

Scientific paper

For a compact Lie group G we define a regularized version of the Dolbeault cohomology of a G-equivariant holomorphic vector bundles over non-compact Kahler manifolds. The new cohomology is infinite-dimensional, but as a representation of G it decomposes into a sum of irreducible components, each of which appears in it with finite multiplicity. Thus equivariant Betti numbers are well defined. We study various properties of the new cohomology and prove that it satisfies a Kodaira-type vanishing theorem.

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