Finitely presented simple groups with no piecewise projective actions
Group Theory
2025-12-23 v1 Dynamical Systems
Abstract
We construct an explicit infinite family of pairwise non-isomorphic infinite simple groups of type (in particular, they are finitely presented) that act faithfully on the circle by orientation-preserving homeomorphisms, but that admit no non-trivial piecewise affine nor piecewise projective actions on the projective line. Our examples are certain forest-skein groups which, informally, are a mixture of Richard Thompson's groups with Vaughan Jones' planar algebras.
Cite
@article{arxiv.2512.18943,
title = {Finitely presented simple groups with no piecewise projective actions},
author = {Arnaud Brothier and Ryan Seelig},
journal= {arXiv preprint arXiv:2512.18943},
year = {2025}
}
Comments
32 pages, 18 figures, this article is a shorter self-contained version of arXiv:2411.12569 focused on witnessing corollary F, to appear in J. Lond. Math. Soc