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\iteman{io-port 05996752}
\itemau{Gonz\'alez-Meneses, Juan; Wiest, Bert}
\itemti{Reducible braids and Garside theory.}
\itemso{Algebr. Geom. Topol. 11, No. 5, 2971-3010 (2011).}
\itemab
Summary: 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 Nielsen-Thurston type of any braid, modulo one well-known conjecture on the speed of convergence of the cyclic sliding operation.
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\itemcc{}
\itemut{braid groups; Garside groups; reducible braids; Nielsen-Thurston classification; polynomial time algorithms; polynomial time complexity; cyclic sliding operation; conjugacy classes}
\itemli{doi:10.2140/agt.2011.11.2971}
\end