Deformation problems in Lie groupoids

• Autor(a) principal: Cárdenas, Cristian Camilo Cárdenas
• Data de Publicação: 2018
• Tipo de documento: Tese
• Idioma: eng
• Título da fonte: Biblioteca Digital de Teses e Dissertações da USP
• Texto Completo: http://www.teses.usp.br/teses/disponiveis/45/45131/tde-24072019-165047/
• topic: Deformações; Deformations; Grupoides simpléticos; Lie groupoid morphisms; Lie subgroupoids; Morfismos de grupoides de Lie; Subgrupoides de Lie; Symplectic groupoids

In this thesis we present the deformation theory of Lie groupoid morphisms, Lie subgroupoids and symplectic groupoids. The corresponding deformation complexes governing such deformations are defined and used to investigate a Moser argument in each of these contexts. We also apply this theory to the case of Lie group morphisms and Lie subgroups, obtaining rigidity results of these structures. Moreover, in the case of symplectic groupoids, we define a map between the differentiable and deformation cohomology of the underlying groupoid, which is regarded as the global counterpart of a map $i$ defined by Crainic and Moerdijk (2004) which relates the (Poisson) cohomology of the Poisson structure on the base $M$ of the groupoid to the deformation cohomology of the Lie algebroid $T^{*}M$ associated to it.