Finitely presented simple groups with no piecewise projective actions
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866918258902302720 |
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| author | Brothier, Arnaud Seelig, Ryan |
| author_facet | Brothier, Arnaud Seelig, Ryan |
| contents | We construct an explicit infinite family of pairwise non-isomorphic infinite simple groups of type $\mathrm{F}_\infty$ (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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_18943 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Finitely presented simple groups with no piecewise projective actions Brothier, Arnaud Seelig, Ryan Group Theory Dynamical Systems 20E32 We construct an explicit infinite family of pairwise non-isomorphic infinite simple groups of type $\mathrm{F}_\infty$ (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. |
| title | Finitely presented simple groups with no piecewise projective actions |
| topic | Group Theory Dynamical Systems 20E32 |
| url | https://arxiv.org/abs/2512.18943 |