Geodesic
On the genericity of pseudo-Anosov braids II: conjugations to rigid braids
Sandrine Caruso1 ; Bert Wiest2
1Université Rennes 1, France
2Université de Rennes I, France
Groups, geometry, and dynamics, Tome 11 (2017) no. 2, pp. 549-565

Voir la notice de l'article provenant de la source EMS Press

DOI

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⩾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.
DOI : 10.4171/ggd/407
Classification : 20-XX
Mots-clés : Braid group, mapping class group, Garside group, pseudo-Anosov, rigid braid

Sandrine Caruso  1   ; Bert Wiest  2

1 Université Rennes 1, France
2 Université de Rennes I, France 
Sandrine Caruso; Bert Wiest. On the genericity of pseudo-Anosov braids II: conjugations to rigid braids. Groups, geometry, and dynamics, Tome 11 (2017) no. 2, pp. 549-565. doi: 10.4171/ggd/407
@article{10_4171_ggd_407,
     author = {Sandrine Caruso and Bert Wiest},
     title = {On the genericity of {pseudo-Anosov} braids {II:} conjugations to rigid braids},
     journal = {Groups, geometry, and dynamics},
     pages = {549--565},
     year = {2017},
     volume = {11},
     number = {2},
     doi = {10.4171/ggd/407},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/ggd/407/}
}
TY  - JOUR
AU  - Sandrine Caruso
AU  - Bert Wiest
TI  - On the genericity of pseudo-Anosov braids II: conjugations to rigid braids
JO  - Groups, geometry, and dynamics
PY  - 2017
SP  - 549
EP  - 565
VL  - 11
IS  - 2
UR  - http://geodesic.mathdoc.fr/articles/10.4171/ggd/407/
DO  - 10.4171/ggd/407
ID  - 10_4171_ggd_407
ER  - 
%0 Journal Article
%A Sandrine Caruso
%A Bert Wiest
%T On the genericity of pseudo-Anosov braids II: conjugations to rigid braids
%J Groups, geometry, and dynamics
%D 2017
%P 549-565
%V 11
%N 2
%U http://geodesic.mathdoc.fr/articles/10.4171/ggd/407/
%R 10.4171/ggd/407
%F 10_4171_ggd_407

Cité par Sources :