Conjugacy problem for braid groups and Garside groups1
By N. Franco, Juan González-Meneses. 2001
115 citations recorded by the source corpus.
Abstract We present a new algorithm to solve the conjugacy problem in Artin braid groups, which is faster than the one presented by Birman, Ko, and Lee [Adv. Math. 139 (1998) 322–353]. This algorithm can be applied not only to braid groups, but to all Garside groups (which include finite type Artin groups and torus knot groups among others).
Subfields: Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/183072c4b42477bdde6b51941fa9b1fad3d9cf2d
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In Geometry and Topology
In Mathematical Physics
Citations in the corpus
- Basic results on braid groups (2010, methodology): “There have been several improvements of this algorithm, all of them using these techniques pioneered by Garside[30, 12, 36, 38, 10, 39, 40].”
- Conjugacy in Garside groups II: structure of the ultra summit set (2006, methodology): “Nevertheless, the theoretical complexity of the algorithm in [18] is not worse than the theoretical complexity of the algorithm in [ 16 ], which is based upon SSS.X/, and the performance of the algorithm is substantially better in practice.”
- The nth root of a braid is unique up to conjugacy (2003, unknown): “rs and relations, given by Artin [1] Bn = ˝ σ1,σ2,...,σn−1 σiσj = σjσi (|i −j| ≥ 2) σiσi+1σi = σi+1σiσi+1 (1 ≤ i ≤ n−2) ˛ , and the solutions to the word problem [11, 20, 3] and the conjugacy problem [7, 3, 9]. Closely related to the latter is the problem of determining the Gc eometry&Topology P”
- The cyclic sliding operation in Garside groups (2008, background): “[15, 8, 17, 19, 5, 6, 7, 22, 23, 24, 26]”
- Foundations of Garside Theory (2013, unknown): “This program turned out to be rather successful and it led to many developments by a number of different authors [8, 11, 12, 16, 18, 17, 48, 47, 59, 111, 118, 127, 128, 158, 157, 165, 181, 192, ...].”
- Conjugacy in Garside groups I: cyclings, powers and rigidity (2006, background): “Each algorithm in [23], [20], [22], [24] is an improvement of the previous one, but the basic idea is the same in all of them: Given an element X 2 G, the algorithm computes a finite subset IX of the conjugacy class of X which has the following properties: (1) For every X 2 G, the set IX is finite, ”