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Dual Garside structure and reducibility of braids


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Author: Calvez, Matthieu
Department: Universidad de Sevilla. Departamento de álgebra
Date: 2012-04-15
Published in: Journal of Algebra, 356 (1), 355-373.
Document type: Article
Abstract: 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.
Cite: Calvez, M. (2012). Dual Garside structure and reducibility of braids. Journal of Algebra, 356 (1), 355-373.
Size: 342.2Kb
Format: PDF


DOI: 10.1016/j.jalgebra.2012.01.022

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