Background Cohomology and Symplectic Reduction
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866913571127951360 |
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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 |