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...
| Autor: | |
|---|---|
| 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 |
| 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. |
|---|