Work

Dynamics on the $\mathrm {SU}(2,1)$ -character variety of the one-holed torus

Year: 2025

Type: article

Abstract: We study the relative $\mathrm {SU}(2,1)$ -character varieties of the one-holed torus, and the action of the mapping class group on them. We use an explicit description of the character variety of the free group of rank two in $\mathrm {SU}(2,1)$ in terms of traces, which allow us to describe the topology of the character variety. We then combine this description with a generalization of the Farey graph adapted to this new combinatorial setting, using ideas introduced by Bowditch. Using these tools, we can describe an open domain of discontinuity for the action of the mapping class group which strictly contains the set of convex cocompact characters, and we give several characterizations of representations in this domain.

Source: Moduli

DOI: 10.1112/mod.2025.3

Authors: Sean Lawton, Sara Maloni, Frédéric Palesi

Language: English

Topic: Geometric and Algebraic Topology

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $3,450

Funder: National Science Foundation

Awards: CAREER: Geometric Structures, Character Varieties, and Higher Teichmuller Theory, RNMS: Geometric structures and representation varieties, RNMS: Geometric Structures and Representation Varieties