scholarly journals Pappus Theorem, Schwartz Representations and Anosov Representations

2018 ◽  
Vol 68 (6) ◽  
pp. 2697-2741
Author(s):  
Thierry Barbot ◽  
Gye-Seon Lee ◽  
Viviane Pardini Valério
Keyword(s):  
Anosov Representations

scholarly journals Topological invariants of Anosov representations

2010 ◽  
Vol 3 (3) ◽  
pp. 578-642 ◽  
Author(s):  
Olivier Guichard ◽  
Anna Wienhard
Keyword(s):  
Topological Invariants ◽  
Anosov Representations

scholarly journals Topological restrictions on Anosov representations

2020 ◽  
Vol 13 (4) ◽  
pp. 1497-1520
Author(s):  
Richard Canary ◽  
Konstantinos Tsouvalas
Keyword(s):  
Anosov Representations

scholarly journals SOME RECENT RESULTS ON ANOSOV REPRESENTATIONS

2016 ◽  
Vol 21 (4) ◽  
pp. 1105-1121 ◽  
Author(s):  
MICHAEL KAPOVICH ◽  
BERNHARD LEEB ◽  
JOAN PORTI
Keyword(s):  
Anosov Representations

Model Higgs bundles in exceptional components of the Sp(4, ℝ)-character variety

2021 ◽  
pp. 2150067
Author(s):  
Georgios Kydonakis
Keyword(s):  
Elliptic Operator ◽  
Moduli Space ◽  
Riemann Surfaces ◽  
Higgs Bundle ◽  
Character Variety ◽  
Topological Invariants ◽  
Higgs Bundles ◽  
Connected Sum ◽  
Anosov Representations

We establish a gluing construction for Higgs bundles over a connected sum of Riemann surfaces in terms of solutions to the [Formula: see text]-Hitchin equations using the linearization of a relevant elliptic operator. The construction can be used to provide model Higgs bundles in all the [Formula: see text] exceptional components of the maximal [Formula: see text]-Higgs bundle moduli space, which correspond to components solely consisting of Zariski dense representations. This also allows a comparison between the invariants for maximal Higgs bundles and the topological invariants for Anosov representations constructed by Guichard and Wienhard.

scholarly journals On Borel Anosov representations in even dimensions

2020 ◽  
Vol 95 (4) ◽  
pp. 749-763
Author(s):  
Konstantinos Tsouvalas
Keyword(s):  
Anosov Representations

scholarly journals An introduction to pressure metrics for higher Teichmüller spaces

2017 ◽  
Vol 38 (6) ◽  
pp. 2001-2035 ◽  
Author(s):  
MARTIN BRIDGEMAN ◽  
RICHARD CANARY ◽  
ANDRÉS SAMBARINO
Keyword(s):  
Hyperbolic Group ◽  
Thermodynamic Formalism ◽  
Orientable Surface ◽  
Open Problems ◽  
Closed Orientable Surface ◽  
Teichmüller Spaces ◽  
Teichmuller Spaces ◽  
Word Hyperbolic Group ◽  
Classical Setting ◽  
Anosov Representations

We discuss how one uses the thermodynamic formalism to produce metrics on higher Teichmüller spaces. Our higher Teichmüller spaces will be spaces of Anosov representations of a word-hyperbolic group into a semi-simple Lie group. We begin by discussing our construction in the classical setting of the Teichmüller space of a closed orientable surface of genus at least 2, then we explain the construction for Hitchin components and finally we treat the general case. This paper surveys results of Bridgeman, Canary, Labourie and Sambarino, The pressure metric for Anosov representations, and discusses questions and open problems which arise.

scholarly journals Conformality for a robust class of non-conformal attractors

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Maria Beatrice Pozzetti ◽  
Andrés Sambarino ◽  
Anna Wienhard
Keyword(s):  
Hausdorff Dimension ◽  
Critical Exponent ◽  
Convergence Property ◽  
Limit Set ◽  
Limit Sets ◽  
Differentiability Property ◽  
Anosov Representations

AbstractIn this paper we investigate the Hausdorff dimension of limit sets of Anosov representations. In this context we revisit and extend the framework of hyperconvex representations and establish a convergence property for them, analogue to a differentiability property. As an application of this convergence, we prove that the Hausdorff dimension of the limit set of a hyperconvex representation is equal to a suitably chosen critical exponent.

scholarly journals Anosov representations and proper actions

2017 ◽  
Vol 21 (1) ◽  
pp. 485-584 ◽  
Author(s):  
François Guéritaud ◽  
Olivier Guichard ◽  
Fanny Kassel ◽  
Anna Wienhard
Keyword(s):  
Proper Actions ◽  
Anosov Representations
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