Groups, Geometry, and Dynamics


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Volume 10, Issue 1, 2016, pp. 65–90
DOI: 10.4171/GGD/343

Published online: 2016-02-09

On the space of left-orderings of virtually solvable groups

Cristóbal Rivas[1] and Romain Tessera[2]

(1) Universidad de Santiago de Chile, Chile
(2) Université Paris-Sud, Orsay, France

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 $\operatorname{SOL}=\mathbb Z^2 \rtimes_T \mathbb Z$.

Keywords: Solvable groups, left-orderable groups, space of orderings, one dimensional dynamics

Rivas Cristóbal, Tessera Romain: On the space of left-orderings of virtually solvable groups. Groups Geom. Dyn. 10 (2016), 65-90. doi: 10.4171/GGD/343