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 language | English (US) |
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Pages (from-to) | 448-467 |
Number of pages | 20 |
Journal | Journal of Algebra |
Volume | 261 |
Issue number | 2 |
DOIs | |
State | Published - Mar 15 2003 |
ASJC Scopus subject areas
- Algebra and Number Theory