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