Work

Entropy rigidity for cusped Hitchin representations

Year: 2026

Type: article

Abstract: We establish an entropy rigidity theorem for Hitchin representations of geometrically finite Fuchsian groups which generalizes a theorem of Potrie and Sambarino for Hitchin representations of closed surface groups. In the process, we introduce the class of (1,1,2)‐hypertransverse groups and show for such a group that the Hausdorff dimension of its conical limit set agrees with its (first) simple root entropy, providing a common generalization of results of Bishop and Jones, for Kleinian groups, and Pozzetti, Sambarino, and Wienhard, for Anosov groups. We also introduce the theory of transverse representations of projectively visible groups as a tool for studying discrete subgroups of linear groups that are not necessarily Anosov or relatively Anosov.

Source: Journal of Topology

DOI: 10.1112/topo.70064

Authors: Richard Canary, Tengren Zhang, Andrew Zimmer

Institutions: University of Michigan, National University of Singapore, University of Wisconsin–Madison

Language: English

Topic: Geometric and Algebraic Topology

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,930

Funders: National Science Foundation, Simons Foundation, Ministry of Education, India