Left-orderings on free products of groups (Q420732)

In this interesting paper, the author shows the non-existence of isolated left-orderings on a free product of (left-orderable) groups. In particular, the author shows that the space of left-orderings of a free product of finitely generated groups is homeomorphic to the Cantor set. With the same techniques, the authors give a constructive proof of the fact that the natural conjugation action of the free group (of countable rank greater than one) on its space of left-orderings has a dense orbit.