Publications

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19 Publications visible to you, out of a total of 19

Abstract

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Authors: Federico López, Beatrice Pozzetti, Steve Trettel, Michael Strube, Anna Wienhard

Date Published: 6th Dec 2021

Publication Type: InProceedings

Abstract

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Authors: Federico López, Beatrice Pozzetti, Steve Trettel, Michael Strube, Anna Wienhard

Date Published: 2021

Publication Type: InProceedings

Abstract

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Authors: Federico Lopez, Beatrice Pozzetti, Steve Trettel, Michael Strube, Anna Wienhard

Date Published: 2021

Publication Type: InProceedings

Abstract

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Authors: Daniel Spitz, Jürgen Berges, Markus Oberthaler, Anna Wienhard

Date Published: 2021

Publication Type: Journal

Abstract (Expand)

In this article we define new flows on the Hitchin components for PSL(n,R). 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. We determine a global coordinate system on the Hitchin component. Using the computation of the Goldman symplectic form on the Hitchin component, that is developed by two of the authors in a companion paper to this article (Sun and Zhang in The Goldman symplectic form on the PGL(V)-Hitchin component, 2017. arXiv:1709.03589), this gives a global Darboux coordinate system on the Hitchin component.

Authors: Zhe Sun, Anna Wienhard, Tengren Zhang

Date Published: 1st Apr 2020

Publication Type: Journal

Abstract (Expand)

We introduce coordinates on the space of Lagrangian decorated and framed representations of the fundamental group of a surface with punctures into the symplectic group Sp(2n,R). These coordinates provide a non-commutative generalization of the parametrizations of the spaces of representations into \mathrmSL(2,R) given by Thurston, Penner, and Fock-Goncharov. With these coordinates, the space of framed symplectic representations provides a geometric realization of the non-commutative cluster algebras introduced by Berenstein-Retakh. The locus of positive coordinates maps to the space of decorated maximal representations. We use this to determine the homotopy type of the space of decorated maximal representations, and its homeomorphism type when n=2.

Authors: Daniele Alessandrini, Olivier Guichard, Evgenii Rogozinnikov, Anna Wienhard

Date Published: 2019

Publication Type: Misc

Abstract (Expand)

We study Anosov representation for which the image of the boundary map is the graph of a Lipschitz function, and show that the orbit growth rate with respect to an explicit linear function, the unstable Jacobian, is integral. Several applications to the orbit growth rate in the symmetric space are provided.

Authors: Beatrice Pozzetti, Andrés Sambarino, Anna Wienhard

Date Published: 2019

Publication Type: Misc

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