Lattices on Nonuniform Trees |
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| Authors: | Lisa Carbone Gabriel Rosenberg |
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| Institution: | (1) Department of Mathematics, Hill Center, Busch Campus, Rutgers, The State University of New Jersey, 110 Frelinghuysen Rd, Piscataway, NJ, 08854-8019, U.S.A.;(2) Department of Mathematics, Yale University, 10 Hillhouse Ave, PO Box 208283, New Haven, CT, 06520, U.S.A. |
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| Abstract: | Let X be a locally finite tree, and let G =Aut(X). Then G is a locally compact group. We show that if X has more than one end, and if G contains a discrete subgroup  such that the quotient graph of groups \\X is infinite but has finite covolume, then G contains a nonuniform lattice, that is, a discrete subgroup  such that \G is not compact, yet has a finite G-invariant measure. |
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| Keywords: | lattices trees discrete groups volumes |
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