An irrational-slope Thompson's group
The purpose of this paper is to study the properties of the irrational-slope Thompson's group Fτ introduced by Cleary in [11]. We construct presentations, both finite and infinite, and we describe its combinatorial structure using binary trees. We show that its commutator group is simple. Final...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2021 |
| País: | España |
| Institución: | Universitat Autònoma de Barcelona |
| Repositorio: | Dipòsit Digital de Documents de la UAB |
| Idioma: | catalán |
| OAI Identifier: | oai:ddd.uab.cat:248605 |
| Acceso en línea: | https://ddd.uab.cat/record/248605 https://dx.doi.org/urn:doi:10.5565/PUBLMAT6522112 |
| Access Level: | acceso abierto |
| Palabra clave: | Thompson's group Irrational-slope Normal forms Distortion |
| Sumario: | The purpose of this paper is to study the properties of the irrational-slope Thompson's group Fτ introduced by Cleary in [11]. We construct presentations, both finite and infinite, and we describe its combinatorial structure using binary trees. We show that its commutator group is simple. Finally, inspired by the case of Thompson's group F, we define a unique normal form for the elements of the group and study the metric properties for the elements based on this normal form. As a corollary, we see that several embeddings of F in Fτ are undistorted. |
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