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Bibliographic Details
Main Author: Braverman, Maxim
Format: Preprint
Published: 2024
Subjects:
Online Access:https://arxiv.org/abs/2410.05532
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author Braverman, Maxim
author_facet Braverman, Maxim
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2410_05532
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Background Cohomology and Symplectic Reduction
Braverman, Maxim
Symplectic Geometry
53D20, 32L10, 32Q20
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.
title Background Cohomology and Symplectic Reduction
topic Symplectic Geometry
53D20, 32L10, 32Q20
url https://arxiv.org/abs/2410.05532