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Reducible Suspensions of Anosov Representations
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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.
Forward citations
Cited by 2 Pith papers
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Directional growth of coamenable normal subgroups: counterexamples and rigidity
In higher rank, coamenable normal subgroups preserve the Riemannian critical exponent and growth indicators on the opposition-involution fixed locus but not the full limit cones, with explicit constructions showing th...
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Which reducible representations are Anosov?
A reducible representation is Anosov precisely when the eigenvalue gaps of its irreducible block factors grow at least linearly according to a unique large eigenvalue configuration.
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