A counterexample to the deformation conjecture for uniform tree lattices

Liu, Ying-Sheng

doi:10.1090/S0002-9939-1995-1239799-1

A counterexample to the deformation conjecture for uniform tree lattices
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Proc. Amer. Math. Soc. 123 (1995), 315-319 Request permission

Abstract:

Let X be a universal cover of a finite connected graph. A uniform lattice on X is a group acting discretely and cocompactly on X. We provide a counterexample to Bass and Kulkarni’s Deformation Conjecture (1990) that a discrete subgroup $F \leq \operatorname {Aut} (X)$ could be deformed, outside some F-invariant subtree, into a uniform lattice.

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