arXiv subjects

Ulysse Remfort-Aurat

Publications and source records attributed to Ulysse Remfort-Aurat.

2 recordsLinked to original sources

arXiv2026

Simple-stable representations of surface groups in $\mathrm{PU}(2,1)$

Let $Γ_g$ be the fundamental group of a closed orientable surface of genus $g\geqslant 2$. The outer automorphism group $\mathrm{Out}(Γ_g)$ naturally acts on the character variety $\mathcal{X}(Γ_g,G)$ for any Lie group $G$. We consider the set of simple-stable representations which are modelled on Minsky's primitive-stable representations. We prove that the set of conjugacy classes of simple-stable representations of $Γ_g$ in $\mathrm{PU}(2,1)$ is a domain of discontinuity for this action, strictly larger than the set of conjugacy classes of convex cocompact representations.

math.GT↗

arXiv2023

On some stable representations of hyperbolic groups

Let $Γ$ be a hyperbolic group and G be the isometry group of a Gromov-hyperbolic, properand geodesic metric space. We study the action of the outer automorphism group Out($Γ$) onthe set X($Γ$,G) of conjugacy classes of representations of $Γ$ into G. We construct a familyof Out($Γ$)-invariant subsets of X($Γ$,G) which contains (stricly or not) the set of conjugacyclasses of quasi-convex representations and give a sufficient condition for the induced actionto be properly discontinuous. Finally, we give a criterion for a representation to have discreteimage and finite kernel and use it when G = Isom+(H3) to find new characterizations ofquasi-convex (i.e. convex cocompact) subgroups of PSL2(C).

math.GT↗