A nonamenable type F_∞ group of piecewise projective homeomorphisms

2014/08/13 by Yash Lodha, Lodha, Yash · 1 citation
Computer Science · Mathematics · #FOS: Mathematics #Geometric and Algebraic Topology #Group Theory (math.GR) #Mathematical Dynamics and Fractals #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.1408.3127

openalex publication_date 2014/08/13 · openalex created_date 2017/04/28 · openalex updated_date 2026/07/28

Abstract

We prove that the group of homeomorphisms of the circle introduced by the author with Justin Moore (Groups, Geometry and Dynamics 2015) is of type F_∞. This makes the group the first example of a type F_∞ group which is nonamenable and does not contain nonabelian free subgroups. To prove our result we provide a certain generalisation of cube complexes, which we refer to as cluster complexes. We also obtain a computable normal form, or a canonical unique choice of a word for each element of the group.

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