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arXiv · 2602.14646

Common overlattices in trees and trees with fins

Sam Shepherd
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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.

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Sam Shepherd. 2026-02-16. Common overlattices in trees and trees with fins. https://arxiv.org/abs/2602.14646

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