The boundary rigidity of lattices in products of trees

Abstract

We show that every group acting freely and vertex-transitively by isometries on a product of two regular trees of finite valence is boundary rigid. That means that every CAT(0) space that admits a geometric action of any such group has the visual boundary homeomorphic to a join of two copies of the Cantor set.

10 pages. Upon the revision of the paper, we learned that Margolis (arXiv:2207.04401) proved a much stronger result than our main theorem