Anosov AdS representations are quasi-Fuchsian
Anosov AdS representations are quasi-Fuchsian
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Anosov AdS 表示是准 Fuchsian 的
DOI：
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发表时间：
2007
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通讯作者：
Q. Mérigot
中科院分区：
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作者：
Q. Mérigot
设Gamma是SO（1，n）中的余紧格.一个代表rho：Gamma \to SO（2，n）是拟Fuchsian的，如果它是忠实的，离散的，并且在反德西特空间的边界上保持一个因果子集-一个特殊的情况是Fuchsian表示的情况，即。SO（1，n）中的Gamma包体和SO（2，n）中的SO（1，n）包体的组成。我们证明，如果一个代表是Anosov在Labourie的意义上，那么它也是准Fuchsian。我们还表明，Fuchsian表示是Anosov：事实上，所有准Fuchsian表示是Anosov将证明在第二部分T。巴伯该研究涉及局部反德西特空间的几何：拟Fuchsian表示是全局双曲时空的完整表示，它与乘积R \times Gamma\H^n同构，并在反德西特空间上局部建模。
Let Gamma be a cocompact lattice in SO(1,n). A representation rho: Gamma \to SO(2,n) is quasi-Fuchsian if it is faithfull, discrete, and preserves an acausal subset in the boundary of anti-de Sitter space - a particular case is the case of Fuchsian representations, ie. composition of the inclusions of Gamma in SO(1,n) and of SO(1,n) in SO(2,n). We prove that if a representation is Anosov in the sense of Labourie then it is also quasi-Fuchsian. We also show that Fuchsian representations are Anosov : the fact that all quasi-Fuchsian representations are Anosov will be proved in a second part by T. Barbot. The study involves the geometry of locally anti-de Sitter spaces: quasi-Fuchsian representations are holonomy representations of globally hyperbolic spacetimes diffeomorphic to the product R \times Gamma\H^n and locally modeled on the anti-de Sitter space.