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H 1 Pseudo-Anosov braids are generic

Auteurs : Wiest, Bert (Auteur de la Conférence)
CIRM (Editeur )

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    Résumé : We prove that generic elements of braid groups are pseudo-Anosov, in the following sense: in the Cayley graph of the braid group with $n\geq 3$ strands, with respect to Garside's generating set, we prove that the proportion of pseudo-Anosov braids in the ball of radius $l$ tends to $1$ exponentially quickly as $l$ tends to infinity. Moreover, with a similar notion of genericity, we prove that for generic pairs of elements of the braid group, the conjugacy search problem can be solved in quadratic time. The idea behind both results is that generic braids can be conjugated ''easily'' into a rigid braid.
    braid groups - Garside groups - Nielsen-Thurston classification - pseudo-Anosov - conjugacy problem

    Codes MSC :
    20F10 - Word problems, other decision problems, connections with logic and automata, See also {03B25, 03D05, 03D40, 06B25, 08A50, 68Qxx}
    20F36 - Braid groups; Artin groups
    20F65 - Geometric group theory

      Informations sur la Vidéo

      Langue : Anglais
      Date de publication : 28/05/14
      Date de captation : 02/07/13
      Collection : Research talks ; Algebra ; Combinatorics ; Geometry ; Probability and Statistics ; Topology
      Format : quicktime ; audio/x-aac
      Durée : 00:58:24
      Domaine : Algebra ; Combinatorics ; Probability & Statistics ; Topology ; Geometry
      Audience : Chercheurs ; Doctorants , Post - Doctorants
      Download : https://videos.cirm-math.fr/2013-07-02_Wiest.mp4

    Informations sur la rencontre

    Nom de la rencontre : Low dimensional topology, knots, and orderable groups / Topologie de basse dimension, nœuds et groupes ordonnables
    Organisateurs de la rencontre : Boyer, Steven ; Paris, Luis
    Dates : 01/07/13 - 05/07/13
    Année de la rencontre : 2013
    URL Congrès : http://www.cirm.univ-mrs.fr/RepRenc/862/...

    Citation Data

    DOI : 10.24350/CIRM.V.18576703
    Cite this video as: Wiest, Bert (2013). Pseudo-Anosov braids are generic. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.18576703
    URI : http://dx.doi.org/10.24350/CIRM.V.18576703


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