Opened Access Reducible braids and Garside theory

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Author: González-Meneses López, Juan
Wiest, Bert
Department: Universidad de Sevilla. Departamento de álgebra
Date: 2011
Published in: Algebraic & Geometric Topology, 11 (5), 2971-3010.
Document type: Article
Abstract: We show that reducible braids which are, in a Garside-theoretical sense, as simple as possible within their conjugacy class, are also as simple as possible in a geometric sense. More precisely, if a braid belongs to a certain subset of its conjugacy class which we call the stabilized set of sliding circuits, and if it is reducible, then its reducibility is geometrically obvious: it has a round or almost round reducing curve. Moreover, for any given braid, an element of its stabilized set of sliding circuits can be found using the well-known cyclic sliding operation. This leads to a polynomial time algorithm for deciding the NielsenThurston type of any braid, modulo one well-known conjecture on the speed of convergence of the cyclic sliding operation.
Cite: González-Meneses López, J. y Wiest, B. (2011). Reducible braids and Garside theory. Algebraic & Geometric Topology, 11 (5), 2971-3010.
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