The Diophantine problem in Thompson's group F

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

References in corpus (7)

• Conjugacy and Dynamics in Thompson's Groups
• Foliations for solving equations in groups: free, virtually free, and hyperbolic groups
• Uniform symplicity of groups with proximal action
• Algorithms and Classification in Groups of Piecewise-Linear Homeomorphisms
• Coherence of Associativity in Categories with Multiplication
• Effective equation solving, constraints and growth in virtually abelian groups
• Linear equations with monomial constraints and decision problems in abelian-by-cyclic groups