Ping-pong configurations and circular orders on free groups
| Autor: | Cristóbal Rivas, Kathryn Mann, Michele Triestino, Dominique Malicet |
|---|---|
| Přispěvatelé: | Laboratoire d'Analyse et de Mathématiques Appliquées (LAMA), Université Paris-Est Marne-la-Vallée (UPEM)-Fédération de Recherche Bézout-Université Paris-Est Créteil Val-de-Marne - Paris 12 (UPEC UP12)-Centre National de la Recherche Scientifique (CNRS), Brown University, Universidad de Santiago de Chile [Santiago] (USACH), Institut de Mathématiques de Bourgogne [Dijon] (IMB), Université de Bourgogne (UB)-Centre National de la Recherche Scientifique (CNRS), FONDECYT 1150691, PEPS – Jeunes Chercheur-e-s – 2017 (CNRS), Projet 'Jeunes Géométres' of F. Labourie (financed by the Louis D. Foundation), Réseau France-Brésil en Mathématiques., NSF grant DMS-1606254, Université de Bourgogne (UB)-Université Bourgogne Franche-Comté [COMUE] (UBFC)-Centre National de la Recherche Scientifique (CNRS), Centre National de la Recherche Scientifique (CNRS)-Université Paris-Est Créteil Val-de-Marne - Paris 12 (UPEC UP12)-Fédération de Recherche Bézout-Université Paris-Est Marne-la-Vallée (UPEM), Centre National de la Recherche Scientifique (CNRS)-Université de Franche-Comté (UFC), Université Bourgogne Franche-Comté [COMUE] (UBFC)-Université Bourgogne Franche-Comté [COMUE] (UBFC)-Université de Bourgogne (UB), Laboratoire d'Analyse et de Mathématiques Appliquées ( LAMA ), Université Paris-Est Marne-la-Vallée ( UPEM ) -Fédération de Recherche Bézout-Université Paris-Est Créteil Val-de-Marne - Paris 12 ( UPEC UP12 ) -Centre National de la Recherche Scientifique ( CNRS ), Universidad de Santiago de Chile [Santiago] ( USACH ), Institut de Mathématiques de Bourgogne [Dijon] ( IMB ), Université de Bourgogne ( UB ) -Centre National de la Recherche Scientifique ( CNRS ) |
| Rok vydání: | 2017 |
| Předmět: |
[ MATH.MATH-GR ] Mathematics [math]/Group Theory [math.GR]
[ MATH.MATH-DS ] Mathematics [math]/Dynamical Systems [math.DS] [MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS] MSC2010: Primary 20F60 57M60. Secondary 20E05 37C85 37E05 37E10 57M60 Extension (predicate logic) Group Theory (math.GR) Dynamical Systems (math.DS) Space (mathematics) 20F60 57M60 [MATH.MATH-GR]Mathematics [math]/Group Theory [math.GR] Combinatorics Free groups One-dimensional dynamics Free group Ping pong FOS: Mathematics Discrete Mathematics and Combinatorics Order (group theory) Geometry and Topology Mathematics - Dynamical Systems Mathematics - Group Theory Mathematics Orders on groups |
| Zdroj: | Groups Geometry and Dynamics Groups Geometry and Dynamics, European Mathematical Society, In press, 13 (4), pp.1195-1218. ⟨10.4171/GGD/519⟩ Groups, Geometry, and Dynamics Groups, Geometry, and Dynamics, 2019, 13 (4), pp.1195-1218. ⟨10.4171/GGD/519⟩ Groups, Geometry, and Dynamics, European Mathematical Society, 2019, 13 (4), pp.1195-1218. ⟨10.4171/GGD/519⟩ |
| ISSN: | 1661-7207 1661-7215 |
| DOI: | 10.48550/arxiv.1709.02348 |
| Popis: | We discuss actions of free groups on the circle with "ping-pong" dynamics; these are dynamics determined by a finite amount of combinatorial data, analogous to Schottky domains or Markov partitions. Using this, we show that the free group $F_n$ admits an isolated circular order if and only if n is even, in stark contrast with the case for linear orders. This answers a question from (Mann, Rivas, 2016). Inspired by work of Alvarez, Barrientos, Filimonov, Kleptsyn, Malicet, Menino and Triestino, we also exhibit examples of "exotic" isolated points in the space of all circular orders on $F_2$. Analogous results are obtained for linear orders on the groups $F_n \times \mathbb{Z}$. Comment: 17 pages. v2 contains many small corrections |
| Databáze: | OpenAIRE |
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