One-dimensional actions of Higman's group
Abstract
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 the Higman 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.
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