One-Dimensional Actions of Higman’S Group

We build a faithful action of Higman’s group on the line by homeomorphisms, answering a question of Yves de Cornulier. As a by-product we obtain many quasimorphisms from Higman’s group into the reals. We also show that every action by C1-diffeomorphisms of Higman’s group on the line or the circle is trivial © Licensed under a Creative Commons Attribution License (CC-BY)