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Dual Garside structure and reducibility of braids

Opened Access Dual Garside structure and reducibility of braids

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Autor: Calvez, Matthieu
Departamento: Universidad de Sevilla. Departamento de álgebra
Fecha: 2012-04-15
Publicado en: Journal of Algebra, 356 (1), 355-373.
Tipo de documento: Artículo
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 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.
Cita: Calvez, M. (2012). Dual Garside structure and reducibility of braids. Journal of Algebra, 356 (1), 355-373.
Tamaño: 342.2Kb
Formato: PDF

URI: http://hdl.handle.net/11441/47530

DOI: 10.1016/j.jalgebra.2012.01.022

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