Amenability and hyperfiniteness for group actions on trees
By Pieter Spaas
Laminations and structure theorems for group actions on the line - Part 1
By Michele Triestino
By Bert Wiest
Appears in collection : Low dimensional topology, knots, and orderable groups / Topologie de basse dimension, nœuds et groupes ordonnables
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