Special elliptic isometries, relative SU(2,1)-character varieties, and bendings

TL;DR

This paper classifies relations among special elliptic isometries in complex hyperbolic geometry, explores relative SU(2,1)-character varieties of the quadruply punctured sphere, and applies these to understand length 5 relations.

Contribution

It provides a complete classification of certain length relations among elliptic isometries and analyzes specific character varieties related to punctured spheres.

Findings

Relations of lengths 2, 3, and 4 are fully classified.

Some relative SU(2,1)-character varieties are described.

Applications to length 5 relations are demonstrated.

Abstract

We study relations between special elliptic isometries in the complex hyperbolic plane. Relations of lengths 2, 3, and 4 are fully classified. Some relative SU(2,1)-character varieties of the quadruply punctured sphere are described and applied to the study of length 5 relations.