Work

Reducible suspensions of Anosov representations

Year: 2025

Type: article

Abstract: We study through the lens of Anosov representations the dynamical properties of reducible suspensions of linear representations of non-elementary hyperbolic groups, which are linear representations preserving and acting weakly unipotently on a proper non-zero subspace. We characterize when reducible suspensions are discrete and (almost) faithful, quasi-isometrically embedded, and Anosov. Anosov reducible suspensions correspond to points in bounded convex domains in a finite-dimensional real vector space. Stronger characterizations of such domains for symmetric Anosov representations allow us to find deformations of Borel Anosov representations which retain some but not all of the Anosov conditions and to compute examples of non-Anosov limits of Anosov representations.

Source: Groups Geometry and Dynamics

DOI: 10.4171/ggd/858

Author: Max Lahn

Institution: University of Michigan

Language: English

Topic: Geometric and Algebraic Topology

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

Funder: National Science Foundation

Award: Deformation Spaces of Geometric Structures