Behavior of branes under mirror symmetry in the moduli spaces of Higgs bundles
Cohomology of differentiable stacks via representations up to homotopy
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| Author(s): |
Total Authors: 2
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| Affiliation: | [1] Univ Fed Fluminense UFF, Dept Geometria GGM, Rua Prof Marcos w de Freitas Reis S-N, BR-24210201 Niteroi, RJ - Brazil
[2] Univ Sao Paulo, Inst Matemat & Estat IME, Rua Matao 1010, BR-05508090 Sao Paulo, SP - Brazil
Total Affiliations: 2
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| Document type: | Journal article |
| Source: | INTERNATIONAL MATHEMATICS RESEARCH NOTICES; v. 2020, n. 14, p. 4395-4432, JUL 2020. |
| Web of Science Citations: | 1 |
| Abstract | |
We study vector bundles over Lie groupoids, known as VB-groupoids, and their induced geometric objects over differentiable stacks. We establish a fundamental theorem that characterizes VB-Morita maps in terms of fiber and basic data, and use it to prove the Morita invariance of VB-cohomology, with implications to deformation cohomology of Lie groupoids and of classic geometries. We discuss applications of our theory to Poisson geometry, providing a new insight over Marsden-Weinstein reduction and the integration of Dirac structures. We conclude by proving that the derived category of VB-groupoids is a Morita invariant, which leads to a notion of VB-stacks, and solves (an instance of) an open question on representations up to homotopy. (AU) | |
| FAPESP's process: | 16/01630-6 - Generalized geometric structure in equivariant Poisson geometry |
| Grantee: | Cristián Andrés Ortiz González |
| Support Opportunities: | Regular Research Grants |