The limit set of subgroups of arithmetic groups in

  • Slavyana Geninska

    Université Paul Sabatier, Toulouse, France

Abstract

We consider subgroups of arithmetic groups in the product with and their limit set. We prove that the projective limit set of a nonelementary finitely generated consists of exactly one point if and only if one and hence all projections of to the simple factors of are subgroups of arithmetic Fuchsian or Kleinian groups. Furthermore, we study the topology of the whole limit set of . In particular, we give a necessary and sufficient condition for the limit set to be homeomorphic to a circle. This result connects the geometric properties of with its arithmetic ones.

Cite this article

Slavyana Geninska, The limit set of subgroups of arithmetic groups in . Groups Geom. Dyn. 8 (2014), no. 4, pp. 1047–1099

DOI 10.4171/GGD/256