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19 Publications visible to you, out of a total of 19
Anosov representations and proper actions

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We establish several characterizations of Anosov representations of word hyperbolic groups into real reductive Lie groups, in terms of a Cartan projection or Lyapunov projection of the Lie group. Using … a properness criterion of Benoist and Kobayashi, we derive applications to proper actions on homogeneous spaces of reductive groups.

Authors: François Guéritaud, Olivier Guichard, Fanny Kassel, Anna Wienhard

Date Published: 2017

Publication Type: Journal

Flows on the PGL(V)-Hitchin component

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In this article we define new flows on the Hitchin components for \mathrmPGL(V). Special examples of these flows are associated to simple closed curves on the surface and give generalized twist flows. … Other examples, so called eruption flows, are associated to pair of pants in S and capture new phenomena which are not present in the case when n = 2. Using these flows, we construct a global coordinate system on the Hitchin component. In a companion paper to this article two of the authors develop new tools to compute the Goldman symplectic form on the Hitchin component, and prove that this global coordinate system is a Darboux coordinate system.

Authors: Zhe Sun, Anna Wienhard, Tengren Zhang

Date Published: 2017

Publication Type: Misc

On order-preserving representations

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In this article we introduce order preserving representations of fundamental groups of surfaces into Lie groups with bi-invariant orders. By relating order preserving representations to weakly maximal … representations, introduced in arXiv:1305.2620, we show that order preserving representations into Lie groups of Hermitian type are faithful with discrete image and that the set of order preserving representations is closed in the representation variety. For Lie groups of Hermitian type whose associated symmetric space is of tube type we give a geometric characterization of these representations in terms of the causal structure on the Shilov boundary.

Authors: G. Ben Simon, M. Burger, T. Hartnick, A. Iozzi, A. Wienhard

Date Published: 29th Jun 2016

Publication Type: Journal

Representations and geometric structures

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This note summarizes in an informal way some geometric properties of Anosov representations into the symplectic group, which were presented in a talk at the conference What is Next. The mathematical … legacy of Bill Thurston, held in June 2014 in Cornell.

Author: Anna Wienhard

Date Published: 2016

Publication Type: Misc

Compactification of certain Clifford-Klein forms of reductive homogeneous spaces

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We describe smooth compactifications of certain families of reductive homogeneous spaces such as group manifolds for classical Lie groups, or pseudo-Riemannian analogues of real hyperbolic spaces and … their complex and quaternionic counterparts. We deduce compactifications of Clifford-Klein forms of these homogeneous spaces, namely quotients by discrete groups Gamma acting properly discontinuously, in the case that Gamma is word hyperbolic and acts via an Anosov representation. In particular, these Clifford-Klein forms are topologically tame.

Authors: François Guéritaud, Olivier Guichard, Fanny Kassel, Anna Wienhard

Date Published: 2015

Publication Type: Misc

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