activity
20072024
most citedAnosov representations: Domains of discontinuity and applications

166 citations · 346 across the 12 of their papers we have counts for

collaborators

12 papers

math.DG2024★ 1 cited

Positivity, cross-ratios and the Collar Lemma

Jonas Beyrer, Olivier Guichard, François Labourie +2

We prove that -positive representations of fundamental groups of surfaces (possibly cusped or of infinite type) satisfy a collar lemma, and their associated cross-ratios are pos…

math.DG2022

Parametrizing spaces of positive representations

Olivier Guichard, Eugen Rogozinnikov, Anna Wienhard

Using Lusztig's total positivity in split real Lie groups V. Fock and A. Goncharov have introduced spaces of positive (framed) representations. For general semisimple Lie groups a…

math.DG2021★ 6 cited

Positivity and representations of surface groups

Olivier Guichard, François Labourie, Anna Wienhard

In arXiv:1802.02833 Guichard and Wienhard introduced the notion of -positivity, a generalization of Lusztig's total positivity to real Lie groups that are not necessarily split.…

math.DG2019★ 2 cited

Noncommutative coordinates for symplectic representations

Daniele Alessandrini, Olivier Guichard, Eugen Rogozinnikov +1

We introduce coordinates on the spaces of framed and decorated representations of the fundamental group of a surface with nonempty boundary into the symplectic group $Sp(2n,\mathbf…

math.DG2018★ 3 cited

Positivity and higher Teichmüller theory

Olivier Guichard, Anna Wienhard

We introduce -positivity, a new notion of positivity in real semisimple Lie groups. The notion of -positivity generalizes at the same time Lusztig's total positivity in split…

math.GT2015★ 12 cited

Tameness of Riemannian locally symmetric spaces arising from Anosov representations

Olivier Guichard, Fanny Kassel, Anna Wienhard

We construct compactifications of Riemannian locally symmetric spaces arising as quotients by Anosov representations. These compactifications are modeled on generalized Satake comp…