Pinching surface groups in complex hyperbolic plane

2001/09/22 by Igor Belegradek, Belegradek, Igor
Mathematics · #30F40 #53C55 #57M50 #Algebraic Geometry and Number Theory #Differential Geometry (math.DG) #FOS: Mathematics #Geometric and Algebraic Topology #Mathematical Dynamics and Fractals #math.DG #msc:30F40 #msc:53C55 #msc:57M50

paper · pdf · doi:10.48550/arxiv.math/0109169

this is a revised version of my preprint written in 1995

arxiv created 2001/09/22 · openalex publication_date 2001/09/22 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We construct first examples of discrete geometrically finite subgroups of PU(2,1) which contain parabolic elements, and are isomorphic to surface groups.

Related

• Surface-like boundaries of hyperbolic groups
• Planar boundaries and parabolic subgroups
• On the domination of surface-group representations in PU(2,1)
• Geometric survey of subgroups of mapping class groups
• Cubulating Surface-by-free Groups