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arXiv · 1905.00938

One-dimensional actions of Higman's group

Cristóbal Rivas·Michele Triestino
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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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Cristóbal Rivas, Michele Triestino. 2019-05-02. One-dimensional actions of Higman's group. https://arxiv.org/abs/1905.00938

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