On deformations of free groups in compact Lie groups

Details On deformations of free groups in compact Lie groups On deformations of free groups in compact Lie groups

2006-11-27

arxiv.org/abs/math/0611830v1

Mathematics

Group Theory

Scientific paper

For n>1, a generic n-tuple of elements in a connected compact non-abelian Lie group G generates a free group. G.A. Margulis and G.A. Soifer conjectured that every such tuple can be slightly deformed to one which generates a group which is not virtually free. In this note we prove this conjecture, and actually show that for n>3 and for an arbitrary dense subgroup D, with some restriction on the minimal size of a generating set, the set of deformations of F_n whose image is D is dense in the variety of all deformations. The proof relies on the product replacement method. Using the same ideas we also prove a conjecture of W.M. Goldman on the ergodicity of the action of Out(F_n) on Hom(F_n,G)/G when n>2. For n=2, using calculus, we produce for any pair (a,b) an arbitrarily close pair (a',b') which generates an infinite group which has Serre property (FA) and in particular is not virtually free.

Affiliated with

Also associated with

No associations

Rating

On deformations of free groups in compact Lie groups does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with On deformations of free groups in compact Lie groups, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On deformations of free groups in compact Lie groups will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-23650