We show that the space of left-orderings of a countable virtually solvable group is either finite or homeomorphic to a Cantor set. We also provide an explicit description of the space of left-orderings of SOL=Z2⋊TZ.
Classification :
06-XX, 20-XX, 37-XX
Mots-clés :
Solvable groups, left-orderable groups, space of orderings, one dimensional dynamics
Affiliations des auteurs :
Cristóbal Rivas
1
;
Romain Tessera
2
1
Universidad de Santiago de Chile, Chile
2
Université Paris-Sud, Orsay, France
Cristóbal Rivas; Romain Tessera. On the space of left-orderings of virtually solvable groups. Groups, geometry, and dynamics, Tome 10 (2016) no. 1, pp. 65-90. doi: 10.4171/ggd/343
@article{10_4171_ggd_343,
author = {Crist\'obal Rivas and Romain Tessera},
title = {On the space of left-orderings of virtually solvable groups},
journal = {Groups, geometry, and dynamics},
pages = {65--90},
year = {2016},
volume = {10},
number = {1},
doi = {10.4171/ggd/343},
url = {http://geodesic.mathdoc.fr/articles/10.4171/ggd/343/}
}
TY - JOUR
AU - Cristóbal Rivas
AU - Romain Tessera
TI - On the space of left-orderings of virtually solvable groups
JO - Groups, geometry, and dynamics
PY - 2016
SP - 65
EP - 90
VL - 10
IS - 1
UR - http://geodesic.mathdoc.fr/articles/10.4171/ggd/343/
DO - 10.4171/ggd/343
ID - 10_4171_ggd_343
ER -
%0 Journal Article
%A Cristóbal Rivas
%A Romain Tessera
%T On the space of left-orderings of virtually solvable groups
%J Groups, geometry, and dynamics
%D 2016
%P 65-90
%V 10
%N 1
%U http://geodesic.mathdoc.fr/articles/10.4171/ggd/343/
%R 10.4171/ggd/343
%F 10_4171_ggd_343
