Representations of low copolarity and the orbifold structures of Sp(2) // Sp(1)

• Ano de defesa: 2022
• Autor(a) principal: Gomes, André Magalhães de Sá
• 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: Biquocientes; Biquotients; Compact Lie groups; Copolaridade; Copolarity; Geometria Riemanniana; Grupos de Lie compactos; Orbifolds; Representações de grupos de Lie; Representations of Lie groups; Riemannian Geometry
• Link de acesso: https://www.teses.usp.br/teses/disponiveis/45/45131/tde-05042022-133024/

The aim of this work is twofold. Firstly, we study representations of compact Lie groups from the point of view of their quotient spaces, considered as metric spaces. As result we classified irreducible representations that admit a non-trivial reduction of copolarities varying from 7 to 9. Secondly, we study the connection between biquotients and orbifolds, which still is one of the main techniques used to construct new examples of positively curved orbifolds. As result, we classied the biquotients of Sp(2) from a topological point of view. The Gromoll-Meyer sphere figures among them, which is well-known in the literature. But there is yet two new examples, of which we constructed for one of them a metric of almost-positive curvature.