We show that certain left-orderable groups admit no isolated left orders. The groups we consider are cyclic amalgamations of a free group with a general left-orderable group, the HNN extensions of free groups over cyclic subgroups, and a particular class of one-relator groups. In order to prove the results about orders, we develop perturbation techniques for actions of these groups on the line.
"Spaces of orders of some one-relator groups." Algebr. Geom. Topol. 18 (7) 4161 - 4185, 2018. https://doi.org/10.2140/agt.2018.18.4161