Doctoral Thesis
DOI
https://doi.org/10.11606/T.45.2022.tde-05042022-133024
Document
Author
Full name
André Magalhães de Sá Gomes
E-mail
Institute/School/College
Knowledge Area
Date of Defense
Published
São Paulo, 2022
Supervisor
Committee
Gorodski, Claudio (President)
Gozzi, Francisco Jose
Grama, Lino Anderson da Silva
Silva, Marcos Martins Alexandrino da
Sperança, Llohann Dallagnol
Title in English
Representations of low copolarity and the orbifold structures of Sp(2) // Sp(1)
Keywords in English
Biquotients
Compact Lie groups
Copolarity
Orbifolds
Representations of Lie groups
Riemannian Geometry
Abstract in English
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.
Title in Portuguese
Representações de Baixa Copolaridade e as Estruturas de Orbifold de Sp(2) // Sp(1)
Keywords in Portuguese
Biquocientes
Copolaridade
Geometria Riemanniana
Grupos de Lie compactos
Orbifolds
Representações de grupos de Lie
Abstract in Portuguese
Este trabalho tem dois objetivos. Primeiramente estudamos representações de grupos de Lie compactos pela análise de seu quociente, visto como espaço métrico. Como resultado classificamos representações irredutÃveis e que admitem redução não trivial de copolaridade variando entre 7 e 9. Em segundo lugar estudamos a conexão entre biquocientes e orbifolds, que ainda é um dos principais meios na busca por novos exemplos de orbifolds de curvatura positiva. Como resultado, classificamos do ponto de vista topológico os biquocientes de Sp(2). Dentre estes está a esfera exótica de Gromoll-Meyer, já bastante conhecida na literatura. Mas há também dois novos exemplos, dos quais um foi demonstrado que admite uma métrica de curvatura almost positive.
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Publishing Date
2022-04-27