TY - JOUR
T1 - Les théorèmes d'existence de réseaux associés aux arbres
AU - Carbone, Lisa
N1 - Funding Information:
Acknowledgements. Thanks to C. Weibel for helpful discussions, and to B. Doyon and V. Terras for the French translation. The author was supported in part by NSF grant # DMS-9800604.
PY - 2002/8/1
Y1 - 2002/8/1
N2 - Let X be a locally finite tree, and let G = Aut(X). Then G is a locally compact group. In analogy with Lie groups, Bass and Lubotzky conjectured that G contains lattices, that is, discrete subgroups whose quotient carries a finite invariant measure. Bass and Kulkarni showed that G contains uniform lattices if and only if G is unimodular and G\X is finite. We describe the necessary and sufficient conditions for G to contain lattices, both uniform and non-uniform, answering the Bass-Lubotzky conjectures in full.
AB - Let X be a locally finite tree, and let G = Aut(X). Then G is a locally compact group. In analogy with Lie groups, Bass and Lubotzky conjectured that G contains lattices, that is, discrete subgroups whose quotient carries a finite invariant measure. Bass and Kulkarni showed that G contains uniform lattices if and only if G is unimodular and G\X is finite. We describe the necessary and sufficient conditions for G to contain lattices, both uniform and non-uniform, answering the Bass-Lubotzky conjectures in full.
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U2 - 10.1016/S1631-073X(02)02474-3
DO - 10.1016/S1631-073X(02)02474-3
M3 - Article
AN - SCOPUS:0038053131
SN - 1631-073X
VL - 335
SP - 223
EP - 228
JO - Comptes Rendus Mathematique
JF - Comptes Rendus Mathematique
IS - 3
ER -