Examples of infinite covolume subgroups of PSL(2,R)^r with big limit sets

2011/03/13 by Slavyana Geninska, Geninska, Slavyana · 1 citation
Mathematics · #20H10 (Primary) 11F06 #22E40 (Secondary) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric Topology (math.GT) #Geometry and complex manifolds #Group Theory (math.GR) #Mathematical Dynamics and Fractals #math.GR #math.GT #msc:11F06 #msc:20H10 #msc:22E40

paper · pdf · doi:10.48550/arxiv.1103.2555

21 pages

arxiv created 2011/03/13 · openalex publication_date 2011/03/13 · arxiv updated 2011/03/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We provide examples of finitely generated infinite covolume subgroups of PSL(2,R)^r with a "big" limit set, e.g. that contains an open subset of the geometric boundary. They are given by the so called semi-arithmetic Fuchsian groups admitting modular embeddings.

Cited by

• The limit sets of subgroups of lattices in PSL(2,R)^r

Related

• The limit set of subgroups of arithmetic groups in PSL(2,C)^q × PSL(2,R)^r
• Many Examples of Non-cocompact Fuchsian Groups Sitting in PSL(2,Q)
• Subroups of PSL(3,ℂ) with four lines in general position in its Limit Set
• Counting maximal arithmetic subgroups
• Elementary groups in \PSL(3,\C)