JournalsggdVol. 11, No. 2pp. 549–565

On the genericity of pseudo-Anosov braids II: conjugations to rigid braids

  • Sandrine Caruso

    Université Rennes 1, France
  • Bert Wiest

    Université de Rennes I, France
On the genericity of pseudo-Anosov braids II: conjugations to rigid braids cover
Download PDF

A subscription is required to access this article.

Abstract

We prove that generic elements of braid groups are pseudo-Anosov, in the following sense: in the Cayley graph of the braid group with n3n \geqslant 3 strands, with respect to Garside's generating set, we prove that the proportion of pseudo-Anosov braids in the ball of radius ll tends to 11 exponentially quickly as ll 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.

Cite this article

Sandrine Caruso, Bert Wiest, On the genericity of pseudo-Anosov braids II: conjugations to rigid braids. Groups Geom. Dyn. 11 (2017), no. 2, pp. 549–565

DOI 10.4171/GGD/407