The Boundary Rigidity of Lattices in Products of Trees
Keywords:
boundary rigidity, lattices in products of treesAbstract
We show that every group acting properly and cocompactly by isometries on a product of $n$ bounded valance, bushy trees is boundary rigid. That means that every $\operatorname{CAT}(0)$ space that admits a geometric action of any such group has the visual boundary homeomorphic to a join of $n$ copies of the Cantor set.
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