Geodesic
Centralizers in the R. Thompson group $V_n$
Collin Bleak1 orcid ; Hannah Bowman2 ; Alison Gordon Lynch3 ; Garrett Graham4 ; Jacob Hughes4 ; Francesco Matucci5 orcid ; Eugenia Sapir6
1University of St Andrews, United Kingdom
2New York, USA
3University of Wisconsin, Madison, USA
4University of California, San Diego, La Jolla, USA
5Université Paris-Sud, Orsay, France
6Stanford University, USA
Groups, geometry, and dynamics, Tome 7 (2013) no. 4, pp. 821-865

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

DOI

Let n≥2 and let α∈Vn​ be an element in the Higman–Thompson group Vn​. We study the structure of the centralizer of α∈Vn​ through a careful analysis of the action of 〈α〉 on the Cantor set C. We make use of revealing tree pairs as developed by Brin and Salazar from which we derive discrete train tracks and flow graphs to assist us in our analysis. A consequence of our structure theorem is that element centralizers are finitely generated. Along the way we give a short argument using revealing tree pairs which shows that cyclic groups are undistorted in Vn​.
DOI : 10.4171/ggd/207
Classification : 20-XX, 37-XX
Mots-clés : Conjugacy, centralizer, Thompson's group V, train track, flow graph

Collin Bleak  1   ; Hannah Bowman  2   ; Alison Gordon Lynch  3   ; Garrett Graham  4   ; Jacob Hughes  4   ; Francesco Matucci  5   ; Eugenia Sapir  6

1 University of St Andrews, United Kingdom
2 New York, USA
3 University of Wisconsin, Madison, USA
4 University of California, San Diego, La Jolla, USA
5 Université Paris-Sud, Orsay, France
6 Stanford University, USA 
Collin Bleak; Hannah Bowman; Alison Gordon Lynch; Garrett Graham; Jacob Hughes; Francesco Matucci; Eugenia Sapir. Centralizers in the R. Thompson group $V_n$. Groups, geometry, and dynamics, Tome 7 (2013) no. 4, pp. 821-865. doi: 10.4171/ggd/207
@article{10_4171_ggd_207,
     author = {Collin Bleak and Hannah Bowman and Alison Gordon Lynch and Garrett Graham and Jacob Hughes and Francesco Matucci and Eugenia Sapir},
     title = {Centralizers in the {R.} {Thompson} group $V_n$},
     journal = {Groups, geometry, and dynamics},
     pages = {821--865},
     year = {2013},
     volume = {7},
     number = {4},
     doi = {10.4171/ggd/207},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/ggd/207/}
}
TY  - JOUR
AU  - Collin Bleak
AU  - Hannah Bowman
AU  - Alison Gordon Lynch
AU  - Garrett Graham
AU  - Jacob Hughes
AU  - Francesco Matucci
AU  - Eugenia Sapir
TI  - Centralizers in the R. Thompson group $V_n$
JO  - Groups, geometry, and dynamics
PY  - 2013
SP  - 821
EP  - 865
VL  - 7
IS  - 4
UR  - http://geodesic.mathdoc.fr/articles/10.4171/ggd/207/
DO  - 10.4171/ggd/207
ID  - 10_4171_ggd_207
ER  - 
%0 Journal Article
%A Collin Bleak
%A Hannah Bowman
%A Alison Gordon Lynch
%A Garrett Graham
%A Jacob Hughes
%A Francesco Matucci
%A Eugenia Sapir
%T Centralizers in the R. Thompson group $V_n$
%J Groups, geometry, and dynamics
%D 2013
%P 821-865
%V 7
%N 4
%U http://geodesic.mathdoc.fr/articles/10.4171/ggd/207/
%R 10.4171/ggd/207
%F 10_4171_ggd_207

Cité par Sources :