Morita Equivalences of Vector Bundles

Autor(es)

del Hoyo, Matias ^[1] ; Ortiz, Cristian ^[2]

Afiliação do(s) autor(es)

^[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

• Tipo de documento: Artigo Científico
• Fonte: INTERNATIONAL MATHEMATICS RESEARCH NOTICES; v. 2020, n. 14, p. 4395-4432, JUL 2020.
• Citações Web of Science: 1

Resumo

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)

• Processo FAPESP: 16/01630-6 - Estruturas geométricas generalizadas em geometria de Poisson equivariante
• Beneficiário: Cristián Andrés Ortiz González
• Modalidade de apoio: Auxílio à Pesquisa - Regular