Finitely presented simple groups with no piecewise projective actions
Arnaud Brothier, Ryan Seelig

TL;DR
This paper constructs an infinite family of finitely presented simple groups that act faithfully on the circle but do not admit non-trivial piecewise affine or projective actions, revealing new properties of such groups.
Contribution
It introduces explicit examples of simple groups with specific action restrictions, combining ideas from Thompson groups and planar algebras.
Findings
Constructed infinite simple groups of type F_infinity
Groups act faithfully on the circle by orientation-preserving homeomorphisms
Groups admit no non-trivial piecewise affine or projective actions
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.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsAdvanced Operator Algebra Research · Geometric and Algebraic Topology · Algebraic structures and combinatorial models
