Triangle groups in the complex hyperbolic plane and special fibers of the momentum map in PU(2,1)

2023/04/20 by Marc-Zwecker, Arielle
#Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2304.10329

Abstract

In this work, we consider relative character varieties for representations of the 3-punctured sphere group in PU(2,1). We provide necessary and sufficient conditions on the peripheral conjugacy classes, for such a representation to admit a decomposition as products of special elliptic elements. We prove that the representations satisfying these conditions form fibers of the so-called momentum map for PU(2,1). We apply these results to representations of the even subgroup of triangle groups, and describe components of the associated character variety.

Related

• Complex hyperbolic free groups with many parabolic elements
• Bending Fuchsian representations of fundamental groups of cusped surfaces in PU(2,1)
• Complex Hyperbolic Triangle Groups with 2-fold Symmetry
• On type-preserving representations of the thrice punctured projective plane group
• On the domination of surface-group representations in PU(2,1)