One-dimensional actions of Higman's group

Published 2 May 2019 in math.GR and math.DS | (1905.00938v2)

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 $C^{1$-diffeomorphisms} of Higman's group on the line or the circle is trivial.

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