Les théorèmes d'existence de réseaux associés aux arbres

Translated title of the contribution: The tree lattice existence theorems

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


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.

Translated title of the contributionThe tree lattice existence theorems
Original languageFrench
Pages (from-to)223-228
Number of pages6
JournalComptes Rendus Mathematique
Issue number3
StatePublished - Aug 1 2002

All Science Journal Classification (ASJC) codes

  • Mathematics(all)


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