English

Common overlattices in trees and trees with fins

Group Theory 2026-02-17 v1

Abstract

Bass and Kulkarni proved that any pair of free uniform lattices in the automorphism group of a tree have conjugates that both lie inside a third uniform lattice (which is not necessarily free). We show that this does not generalise to trees with fins. The construction of our counter-example involves working with a certain generalisation of the universal groups of Burger and Mozes.

Keywords

Cite

@article{arxiv.2602.14646,
  title  = {Common overlattices in trees and trees with fins},
  author = {Sam Shepherd},
  journal= {arXiv preprint arXiv:2602.14646},
  year   = {2026}
}

Comments

17 pages, 3 figures