Counting lattices in Aut group of trees

abstract

In constrast to lattices of Lie groups, there are infinite ascending chain of lattices in the automorphism group of trees. We investigate the asymptotics of the number of ``overlattices" of a cocompact lattice in the automorphism group of a locally finite tree. We prove prove an upper bound for general trees and lattices, and a lower bound for certain lattices in some regular trees.

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