Geodesic
The limit set of subgroups of arithmetic groups in $\mathrm{PSL} (2, \mathbb C)^q \times \mathrm{PSL} (2, \mathbb R)^r$
Slavyana Geninska1
1Université Paul Sabatier, Toulouse, France
Groups, geometry, and dynamics, Tome 8 (2014) no. 4, pp. 1047-1099

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DOI

We consider subgroups Γ of arithmetic groups in the product PSL(2,C)q×PSL(2,R)r with q+r≥2 and their limit set. We prove that the projective limit set of a nonelementary finitely generated Γ consists of exactly one point if and only if one and hence all projections of Γ to the simple factors of PSL(2,C)q×PSL(2,R)r are subgroups of arithmetic Fuchsian or Kleinian groups. Furthermore, we study the topology of the whole limit set of Γ. 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 Γ with its arithmetic ones.
DOI : 10.4171/ggd/256
Classification : 20-XX, 22-XX
Mots-clés : Fuchsian groups, arithmetic lattices, limit sets

Slavyana Geninska  1

1 Université Paul Sabatier, Toulouse, France 
Slavyana Geninska. The limit set of subgroups of arithmetic groups in $\mathrm{PSL} (2, \mathbb C)^q \times \mathrm{PSL} (2, \mathbb R)^r$. Groups, geometry, and dynamics, Tome 8 (2014) no. 4, pp. 1047-1099. doi: 10.4171/ggd/256
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     title = {The limit set of subgroups of arithmetic groups in $\mathrm{PSL} (2, \mathbb C)^q \times \mathrm{PSL} (2, \mathbb R)^r$},
     journal = {Groups, geometry, and dynamics},
     pages = {1047--1099},
     year = {2014},
     volume = {8},
     number = {4},
     doi = {10.4171/ggd/256},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/ggd/256/}
}
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