Amenability and Thompson’s group F
Amenability is a group theoretical property consisting in the existence of a finite measure defined on all subsets of the group. The concept is motivated and introduced, and some criteria, characterizations and generalizations are presented. Then, this property is studied in a particular group of ho...
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| Tipo de recurso: | tesis de maestría |
| Fecha de publicación: | 2019 |
| 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:2117/171322 |
| Acceso en línea: | https://hdl.handle.net/2117/171322 |
| Access Level: | acceso abierto |
| Palabra clave: | Group theory Amenability Thompson's group Folner Geometric group theory Cayley graphs Binary trees Grups finits Grups infinits Classificació AMS::20 Group theory and generalizations::20F Special aspects of infinite or finite groups Àrees temàtiques de la UPC::Matemàtiques i estadística::Àlgebra::Teoria de grups |
| Sumario: | Amenability is a group theoretical property consisting in the existence of a finite measure defined on all subsets of the group. The concept is motivated and introduced, and some criteria, characterizations and generalizations are presented. Then, this property is studied in a particular group of homeomorphisms of the interval [0,1], Thompson's group F. This group is introduced, along with its most relevant properties, and some possible Folner sequences are proposed and studied. |
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