Automorphisms of Thompson groups

In this work, based on a Brin's article, we explain the structure of automorphism group of F, via a short exact sequence involving the subgroup of automorphisms of F together with the product of two copies of Thompson s group T. We will use a key theorem by McCleary and Rubin to realize each au...

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Detalles Bibliográficos
Autor: Bergadà Batlles, Roger
Tipo de recurso: tesis de maestría
Fecha de publicación:2021
País:España
Institución:Universitat Politècnica de Catalunya (UPC)
Repositorio:UPCommons. Portal del coneixement obert de la UPC
Idioma:inglés
OAI Identifier:oai:upcommons.upc.edu:2117/348776
Acceso en línea:https://hdl.handle.net/2117/348776
Access Level:acceso abierto
Palabra clave:Geometry, Algebraic
Thompson's groups
Automorphism group
Grups algebraics lineals
Classificació AMS::14 Algebraic geometry::14L Algebraic groups
Àrees temàtiques de la UPC::Matemàtiques i estadística::Geometria::Geometria algebraica
Descripción
Sumario:In this work, based on a Brin's article, we explain the structure of automorphism group of F, via a short exact sequence involving the subgroup of automorphisms of F together with the product of two copies of Thompson s group T. We will use a key theorem by McCleary and Rubin to realize each automorphism as conjugation by a homeomorphism in R. The previous short exact sequence will be obtained by just analyzing which shape these normalizing homeomorphisms must have. A crucial property of F, which we need to prove this theorem by McCleary and Rubin, and which we will use along all this work, is its k-transitivity on dyadic numbers for all k.