The Diophantine problem in Thompson's group F

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 B"uchi and Senger and Ciobanu and Garreta to show the Diophantine problem in free groups and monoids with abelianisation constraints is undecidable.

Publication Details

Journal
ArXiv.org
Published
2025-02-20
Primary Topic
Geometric and Algebraic Topology
Type
article
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article

The Diophantine problem in Thompson's group F

ArXiv.org
Geometric and Algebraic Topology
article

The Diophantine problem in Thompson's group F

article en

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 B\"uchi and Senger and Ciobanu and Garreta to show the Diophantine problem in free groups and monoids with abelianisation constraints is undecidable.

ArXiv.org
Openalex Percentile: Top 42%
Geometric and Algebraic Topology
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The Diophantine problem in Thompson's group F · ArXiv.org (2025) | TGRS Research Map | TGRS