Groups acting on products of locally finite trees

J. O. Button

Groups acting on products of locally finite trees

Group Theory 2026-04-14 v2

Authors: J. O. Button

Abstract

We examine the question of which finitely generated groups act properly on a finite product of locally finite simplicial trees and present evidence in favour of hyperbolic surface groups having such an action. We also give a completely explicit embedding of the genus 2 closed hyperbolic surface group in $SL_2(\mathbb{F}_p(x,y))$ for any prime $p$ .

Keywords

finitely generated groups locally finite trees hyperbolic surface groups SL_2 explicit embedding

Cite

@article{arxiv.2603.06139,
  title  = {Groups acting on products of locally finite trees},
  author = {J. O. Button},
  journal= {arXiv preprint arXiv:2603.06139},
  year   = {2026}
}

Comments

Post publication Brody pointed out a sign error in Theorem 5.4. Thanks a lot. arXiv admin note: substantial text overlap with arXiv:1910.04614

Groups acting on products of locally finite trees

Abstract

Keywords

Cite

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