On the space of left-orderings of virtually solvable groups

Cristóbal Rivas, Romain Tessera

Published 2012-09-14, updated 2013-03-22Version 3

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 $SOL=\Z^2\rtimes_T\Z$.