The limit set of subgroups of arithmetic groups in $PSL(2,C)^q \times PSL(2,R)^r$

Details The limit set of subgroups of arithmetic groups in $PSL(2,C)^q \times PSL(2,R)^r$ The limit set of subgroups of arithmetic groups in $PSL(2,C)^q \times PSL(2,R)^r$

2010-01-11

arxiv.org/abs/1001.1720v1

Mathematics

Group Theory

34 pages

Scientific paper

While lattices in semi-simple Lie groups are studied very well, only little is known about discrete subgroups of infinite covolume. The main class of examples are Schottky groups. Here we investigate some new examples. We consider subgroups $\Gamma$ of arithmetic groups in $PSL(2,C)^q \times PSL(2,R)^r$ with $q+r>1$ and their limit set. We prove that the projective limit set of a nonelementary finitely generated $\Gamma$ consists of exactly one point if and only if one and hence all projections of $\Gamma$ to the simple factors of $PSL(2,C)^q \times PSL(2,R)^r$ are subgroups of arithmetic Fuchsian or Kleinian groups. Furthermore, we study the topology of the whole limit set of $\Gamma$. In particular, we give a necessary and sufficient condition for the limit set to be homeomorphic to a circle.

Affiliated with

Also associated with

No associations

Rating

The limit set of subgroups of arithmetic groups in $PSL(2,C)^q \times PSL(2,R)^r$ 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 The limit set of subgroups of arithmetic groups in $PSL(2,C)^q \times PSL(2,R)^r$, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The limit set of subgroups of arithmetic groups in $PSL(2,C)^q \times PSL(2,R)^r$ will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-719308