paper

The Diophantine problem in Thompson's group F

arXiv:2502.14970 · doi:10.1090/mcom/4113

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.

10 pages, thanks to James Belk and Corentin Bodart for pointing out that F is a centralizer in T, thanks to anonymous referee for helpful comments

The Diophantine problem in Thompson's group F · wovepaper