Deformation problems in Lie groupoids

• Ano de defesa: 2018
• Autor(a) principal: Cárdenas, Cristian Camilo Cárdenas
• Tipo de documento: Tese
• Tipo de acesso: Acesso aberto
• Idioma: eng
• Instituição de defesa: Biblioteca Digitais de Teses e Dissertações da USP
• Palavras-chave em Português: Deformações; Deformations; Grupoides simpléticos; Lie groupoid morphisms; Lie subgroupoids; Morfismos de grupoides de Lie; Subgrupoides de Lie; Symplectic groupoids
• Link de acesso: http://www.teses.usp.br/teses/disponiveis/45/45131/tde-24072019-165047/

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.