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Relatively Anosov representations via flows I: theory

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arxiv 2207.14737 v2 pith:SXKB76JV submitted 2022-07-29 math.GT math.DGmath.DS

Feng Zhu , Andrew Zimmer This is my paper · ORCID
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This is the first in a series of two papers that develops a theory of relatively Anosov representations using the original "contracting flow on a bundle" definition of Anosov representations introduced by Labourie and Guichard-Wienhard. In this paper we will mostly focus on general theory while in the second paper we will focus on examples. In the case of relatively hyperbolic groups, this bundle construction involves several choices: the model Gromov-hyperbolic space the group acts on and the norms on the fibers of the bundle. We use the properties of these bundles to define a subclass of nicely behaved relatively Anosov representations, which we call uniformly relatively Anosov. We also prove a stability result.

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Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Transverse groups preserving proper domains in flag manifolds

    math.RT 2025-07 reject novelty 8.0 of 10

    Transverse groups preserving proper domains in flag manifolds must have limit triples of a single type (Maslov index zero in the tube-type case), but the proof of this key claim contains a false step.

  2. Orbital counting for relatively Anosov groups

    math.DS 2026-07 conditional novelty 5.0 of 10

    Relatively Anosov subgroups satisfy orbital counting and equidistribution with exponential growth rate e^{δR}, generalizing Sambarino's Anosov theorem.

  3. Geometry and Dynamics of Transverse Groups

    math.DS 2025-02 conditional

    A survey of recent work showing that Patterson-Sullivan theory, including shadow lemmas and the Hopf-Tsuji-Sullivan dichotomy, extends to transverse subgroups of SL(d,R), with applications to Anosov and relatively Ano...

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