Dominating Surface Group Representations by Fuchsian Ones
Dominating Surface Group Representations by Fuchsian Ones
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DOI：
10.1093/imrn/rnv275
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发表时间：
2013-11
影响因子：
1
通讯作者：
B. Deroin;Nicolas Tholozan
中科院分区：
文献类型：
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作者：
B. Deroin;Nicolas Tholozan
我们证明，负欧拉特征闭曲面的基本群的表示，其值位于截面曲率以 -1 为界的黎曼流形的等距群中，可以由 Fuchsian 表示支配。此外，我们证明了支配可以是严格的，除非表示是离散的并且忠实地限制在曲率-1的不变的全测地线2平面上。当应用于非极值欧拉类的 PSL(2,R) 表示时，我们的结果在理解封闭反德西特 3 流形空间方面向前迈进了一步。
We prove that a representation from the fundamental group of a closed surface of negative Euler characteristic with values in the isometry group of a Riemannian manifold of sectional curvature bounded by −1 can be dominated by a Fuchsian representation. Moreover, we prove that the domination can be made strict, unless the representation is discrete and faithful in restriction to an invariant totally geodesic 2-plane of curvature −1. When applied to representations into PSL(2,R) of non-extremal Euler class, our result is a step forward in understanding the space of closed anti-de Sitter 3-manifolds.