The space of relative orders and a generalization of Morris indicability theorem

Abstract

We introduce the space of relative orders on a group and show that it is compact whenever the group is finitely generated. We use this to show that if [Formula: see text] is a finitely generated group acting on the line by order preserving homeomorphisms and some stabilizer of a point is a proper and co-amenable subgroup, then [Formula: see text] surjects onto [Formula: see text]. This is a generalization of a theorem of Morris.