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- W1497740606 abstract "Let $Gamma$ be a finitely generated group, and let $op{Rep}(Gamma, SO(2,n))$ be the moduli space of representations of $Gamma$ into $SO(2,n)$ ($n geq 2$). An element $rho: Gamma to SO(2,n)$ of $op{Rep}(Gamma, SO(2,n))$ is textit{quasi-Fuchsian} if it is faithful, discrete, preserves an acausal subset in the conformal boundary $Ein_n$ of the anti-de Sitter space; and if the associated globally hyperbolic anti-de Sitter space is spatially compact - a particular case is the case of textit{Fuchsian representations}, i.e. composition of a faithfull, discrete and cocompact representation $rho_f: Gamma to SO(1,n)$ and the inclusion $SO(1,n) subset SO(2,n)$. In cite{merigot} we proved that quasi-Fuchsian representations are precisely representations which are Anosov as defined in cite{labourie}. In the present paper, we prove that quasi-Fuchsian representations form a connected component of $op{Rep}(Gamma, SO(2,n))$. This is an almost direct corollary of the following result: let $Gamma$ be the fundamental group of a globally hyperbolic spacetime locally modeled on $AdS_n$, and let $rho: Gamma to SO_0(2,n)$ be the holonomy representation. Then, if $Gamma$ is Gromov hyperbolic, the $rho(Gamma)$-invariant achronal limit set in $Ein_n$ is acausal." @default.
- W1497740606 created "2016-06-24" @default.
- W1497740606 creator A5071567822 @default.
- W1497740606 date "2013-01-18" @default.
- W1497740606 modified "2023-09-25" @default.
- W1497740606 title "Deformations of Fuchsian AdS representations are Quasi-Fuchsian" @default.
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