González-Meneses López, JuanWiest, Bert2016-06-152016-06-152011González-Meneses López, J. y Wiest, B. (2011). Reducible braids and Garside theory. Algebraic & Geometric Topology, 11 (5), 2971-3010.1472-27471472-2739http://hdl.handle.net/11441/42251We 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.application/pdfengAttribution-NonCommercial-NoDerivatives 4.0 Internacionalhttp://creativecommons.org/licenses/by-nc-nd/4.0/braid groupGarside groupNielsen–Thurston classificationalgorithminfo:eu-repo/semantics/articleinfo:eu-repo/semantics/openAccesshttps://doi.org/10.2140/agt.2011.11.2971