Artículo
A positive proportion of elements of mapping class groups is pseudo-Anosov
Autor/es | Cumplido Cabello, María
Wiest, Bert |
Departamento | Universidad de Sevilla. Departamento de álgebra |
Fecha de publicación | 2018-03-28 |
Fecha de depósito | 2022-11-08 |
Publicado en |
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Resumen | In the Cayley graph of the mapping class group of a closed surface, with respect to any generating set, we look at a ball of large radius centered on the identity vertex, and at the proportion among the vertices in this ... In the Cayley graph of the mapping class group of a closed surface, with respect to any generating set, we look at a ball of large radius centered on the identity vertex, and at the proportion among the vertices in this ball representing pseudo-Anosov elements. A well-known conjecture states that this proportion should tend to one as the radius tends to infinity. We prove that it stays bounded away from zero. We also prove similar results for a large class of subgroups of the mapping class group. |
Cita | Cumplido Cabello, M. y Wiest, B. (2018). A positive proportion of elements of mapping class groups is pseudo-Anosov. The Bulletin of the London Mathematical Society, 50 (3), 390-394. https://doi.org/10.1112/blms.12148. |
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