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On proper extensions of the conformal group

Mello, Ulisses Lakatos De

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Título:
On proper extensions of the conformal group
Autor: Mello, Ulisses Lakatos De
Orientador: Tal, Fabio Armando
Assuntos: Ação De Grupos Em Superfícies; Entropia Topológica; Grupos Topológicos; Ransitividade; Groups Acting On Surfaces; Topological Entropy; Topological Groups; Transitivity
Notas: Tese (Doutorado)
Descrição: It is proven in this essay that any group of orientation preserving diffeomorphisms acting on the 2-sphere and properly extending the conformal group of Möbius transformations must be at least 4-transitive or, more precisely, arc 4-transitive. This means that any two ordered lists of four distinct points can be mapped one onto the other via a transformation in the group, isotopic to the identity. In addition, it is shown that any such group must always contain an element of positive topological entropy, for which a description as isotopic to a relative pseudo-Anosov homeomorphism of the 4-punctured sphere is provided. Furthermore, an elementary characterisation of the Möbius transformations within the full group of sphere diffeomorphisms is given in terms of transitivity.
DOI: 10.11606/T.45.2022.tde-13092022-115126
Editor: Biblioteca Digital de Teses e Dissertações da USP; Universidade de São Paulo; Instituto de Matemática e Estatística
Data de criação/publicação: 2022-07-15
Formato: Adobe PDF
Idioma: Inglês

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