Background Cohomology and Symplectic Reduction

2024/10/07 by Braverman, Maxim
#32L10 #32Q20 #53D20 #FOS: Mathematics #Symplectic Geometry (math.SG)

paper · doi:10.48550/arxiv.2410.05532

Abstract

We consider a Hamiltonian action of a compact Lie group G on a complete \ka manifold M with a proper moment map. In a previous paper, we defined a regularized version of the Dolbeault cohomology of a G-equivariant holomorphic vector bundle, called the background cohomology. In this paper, we show that the background cohomology of a prequantum line bundle over M `commutes with reduction', i.e. the invariant part of the background cohomology is isomorphic to the usual Dolbeault cohomology of the symplectic reduction.

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