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Non-minimal tree actions and the existence of non-uniform tree lattices

Published online by Cambridge University Press:  17 April 2009

Lisa Carbone
Lisa Carbone
Affiliation:
Department of Mathematics, Hill Center-Busch Campus Rutgers, The State University of New Jersey, 110 Frelinghuysen Rd, Piscataway, NJ 08854–8019, United States of America e-mail: carbonel@math.rutgers.edu
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A uniform tree is a tree that covers a finite connected graph. Let X be any locally finite tree. Then G = Aut(X) is a locally compact group. We show that if X is uniform, and if the restriction of G to the unique minimal G-invariant subtree X0 ⊆ X is not discrete then G contains non-uniform lattices; that is, discrete subgroups Γ for which Γ/G is not compact, yet carries a finite G-invariant measure. This proves a conjecture of Bass and Lubotzky for the existence of non-uniform lattices on uniform trees.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 70 , Issue 2 , October 2004 , pp. 257 - 266
Copyright
Copyright © Australian Mathematical Society 2004

References

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