2011/06/10 by Cristóbal Rivas, Rivas, Cristóbal · 1 citation
Mathematics · #06F15 #20F60 #FOS: Mathematics #Group Theory (math.GR) #math.GR #msc:06F15 #msc:20F60
paper · pdf · doi:10.48550/arxiv.1106.2094
13 pages
arxiv created 2011/06/10 · arxiv updated 2011/06/13
We show that no left-ordering on a free product of (left-orderable) groups is isolated. In particular, we show that the space of left-orderings of free product of finitely generated groups is homeomorphic to the Cantor set. With the same techniques, we also give a new and constructive proof of the fact that the natural conjugation action of the free group (on two or more generators) on its space of left-orderings has a dense orbit.