On Dense Free Subgroups of Lie Groups
نویسندگان
چکیده
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 · dimH . As an application, we obtain a new and elementary proof of a conjecture of Connes and Sullivan on amenable actions, which was first proved by Zimmer.
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تاریخ انتشار 2003