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arXiv · 2502.14970

The Diophantine problem in Thompson's group F

Luna Elliott·Alex Levine
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Abstract

We show that the Diophantine problem in Thompson's group F is undecidable. Our proof uses the facts that F has finite commutator width and rank 2 abelianisation, then uses similar arguments used by Büchi and Senger and Ciobanu and Garreta to show the Diophantine problem in free groups and monoids with abelianisation constraints is undecidable.

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Luna Elliott, Alex Levine. 2025-04-18. The Diophantine problem in Thompson's group F. https://doi.org/10.1090/mcom%2F4113

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