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Multi angle 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 [See also 05C25, 20E08, 57Mxx]

      Informations sur la Vidéo

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

    Informations sur la rencontre

    Nom du congrès : Low dimensional topology, knots, and orderable groups / Topologie de basse dimension, noeuds et groupes ordonnables
    Organisteurs Congrès : 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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