On dense free subgroups of Lie groups

E. Breuillard*, T. Gelander

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

70 Scopus citations

Abstract

We give a method for constructing dense and free subgroups in real Lie groups. In particular we show that any dense subgroup of a connected semisimple real Lie group G contains a free group on two generators which is still dense in G, and that any finitely generated dense subgroup in a connected non-solvable Lie group H contains a dense free subgroup of rank ≤ 2 · dim H. This answers a question of Carriere and Ghys, and it gives an elementary proof to a conjecture of Connes and Sullivan on amenable actions, which was first proved by Zimmer.

Original languageEnglish (US)
Pages (from-to)448-467
Number of pages20
JournalJournal of Algebra
Volume261
Issue number2
DOIs
StatePublished - Mar 15 2003

ASJC Scopus subject areas

  • Algebra and Number Theory

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