Reducible Suspensions of Anosov Representations (2312.09886v2)
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.
- Thierry Barbot “Flag structures on Seifert manifolds” In Geometry & Topology 5.1, 2001, pp. 227–266 DOI: 10.2140/gt.2001.5.227
- Thierry Barbot “Three-dimensional Anosov flag manifolds” In Geometry & Topology 14.1, 2010, pp. 153–191 DOI: 10.2140/gt.2010.14.153
- Jairo Bochi, Rafael Potrie and Andrés Sambarino “Anosov representations and dominated splittings” In Journal of the European Mathematical Society 21.11, 2019, pp. 3343–3414 DOI: 10.4171/JEMS/905
- “Displacing Representations and Orbit Maps” In Geometry, Rigidity, and Group Actions, Chicago Lectures in Mathematics Chicago: The University of Chicago Press, 2011, pp. 494–514
- “Anosov representations and proper actions” In Geometry & Topology 21.1, 2017, pp. 485–584 DOI: 10.2140/gt.2017.21.485
- “Anosov representations: domains of discontinuity and applications” In Inventiones mathematicae 190.2, 2012, pp. 357–438 DOI: 10.1007/s00222-012-0382-7
- Michael Kapovich “Hyperbolic Manifolds and Discrete Groups”, Modern Birkhäuser Classics Boston, MA: Birkhäuser, 2010 DOI: 10.1007/978-0-8176-4913-5
- Michael Kapovich, Bernhard Leeb and Joan Porti “Anosov subgroups: dynamical and geometric characterizations” In European Journal of Mathematics 3.4, 2017, pp. 808–898 DOI: 10.1007/s40879-017-0192-y
- Michael Kapovich, Bernhard Leeb and Joan Porti “A Morse lemma for quasigeodesics in symmetric spaces and euclidean buildings” In Geometry & Topology 22.7, 2018, pp. 3827–3923 DOI: 10.2140/gt.2018.22.3827
- “A proof of Selberg’s conjecture” In Mathematics of the USSR-Sbornik 4.1, 1968, pp. 147–152 DOI: 10.1070/SM1968v004n01ABEH002782
- “Eigenvalue gaps for hyperbolic groups and semigroups” In Journal of Modern Dynamics 18, 2022, pp. 161–208 DOI: 10.3934/jmd.2022008
- François Labourie “Anosov flows, surface groups and curves in projective space” In Inventiones mathematicae 165.1, 2006, pp. 51–114 DOI: 10.1007/s00222-005-0487-3
- Seán McGarraghy “Symmetric Powers of Symmetric Bilinear Forms” In Algebra Colloquium 12.1, 2005, pp. 41–57 DOI: 10.1142/S1005386705000052
- Atle Selberg “On discontinuous groups in higher-dimensional symmetric spaces” In Contributions to Function Theory Bombay: Tata Institute of Fundamental Research, 1962, pp. 147–164
- Konstantinos Tsouvalas “Anosov representations, strongly convex cocompact groups and weak eigenvalue gaps”, 2022 DOI: 10.48550/arXiv.2008.04462
- Hans Zassenhaus “Beweis eines satzes über diskrete gruppen” In Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg 12.1, 1937, pp. 289–312 DOI: 10.1007/BF02948950
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