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Mathematics > Group Theory

arXiv:1408.3127 (math)
[Submitted on 13 Aug 2014 (v1), last revised 16 Sep 2020 (this version, v5)]

Title:A nonamenable type $F_{\infty}$ group of piecewise projective homeomorphisms

Authors:Yash Lodha
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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 $F_{\infty}$. This makes the group the first example of a type $F_{\infty}$ 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.
Comments: 72 Pages. Referee comments have been incorporated. To appear in the Journal of Topology
Subjects: Group Theory (math.GR)
Cite as: arXiv:1408.3127 [math.GR]
  (or arXiv:1408.3127v5 [math.GR] for this version)
  https://doi.org/10.48550/arXiv.1408.3127

Submission history

From: Yash Lodha [view email]
[v1] Wed, 13 Aug 2014 20:06:18 UTC (47 KB)
[v2] Wed, 22 Oct 2014 16:46:08 UTC (47 KB)
[v3] Tue, 11 Apr 2017 12:42:19 UTC (55 KB)
[v4] Sun, 21 May 2017 16:39:40 UTC (59 KB)
[v5] Wed, 16 Sep 2020 12:02:36 UTC (66 KB)
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