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