Artículo
Dual Garside structure and reducibility of braids
Autor/es | Calvez, Matthieu |
Departamento | Universidad de Sevilla. Departamento de álgebra |
Fecha de publicación | 2012-04-15 |
Fecha de depósito | 2016-10-14 |
Publicado en |
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Resumen | Benardete, Gutierrez and Nitecki showed an important result which relates the geometrical properties of a braid, as a homeomorphism of the punctured disk, to its algebraic Garside-theoretical properties. Namely, they showed ... Benardete, Gutierrez and Nitecki showed an important result which relates the geometrical properties of a braid, as a homeomorphism of the punctured disk, to its algebraic Garside-theoretical properties. Namely, they showed that if a braid sends a standard curve to another standard curve, then the image of this curve after each factor of the left normal form of the braid (with the classical Garside structure) is also standard. We provide a new simple, geometric proof of the result by Benardete-Gutierrez-Nitecki, which can be easily adapted to the case of the dual Garside structure of braid groups, with the appropriate definition of standard curves in the dual setting. This yields a new algorithm for determining the Nielsen-Thurston type of braids. |
Agencias financiadoras | Université Européenne de Bretagne Junta de Andalucía |
Identificador del proyecto | FQM-218 |
Cita | Calvez, M. (2012). Dual Garside structure and reducibility of braids. Journal of Algebra, 356 (1), 355-373. |
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