论文标题
在$ \ mathrm {psl} _2（\ mathbb {c}）$中，将表面组表示为$ \ mathrm {psl} _2
Dominating surface-group representations into $\mathrm{PSL}_2 (\mathbb{C})$ in the relative representation variety
论文作者
论文摘要
令$ρ$作为刺穿表面的基本组的代表$ \ mathrm {psl} _2（\ mathbb {c}）$，不是Fuchsian。我们证明存在一种紫红色的表示，该表示在简单的长度频谱中严格占主导地位，并保留边界长度。这将Gueritaud-Kassel-Wolff的结果扩展到$ \ Mathrm {psl} _2（\ Mathbb {C}）$ - 表示的情况。我们的证明涉及在$ \ Mathbb {h}^3 $中拉直平面，由框架表示的Fock-Goncharov坐标确定，并应用带状信息。
Let $ρ$ be a representation of the fundamental group of a punctured surface into $\mathrm{PSL}_2 (\mathbb{C})$ that is not Fuchsian. We prove that there exists a Fuchsian representation that strictly dominates $ρ$ in the simple length spectrum, and preserves the boundary lengths. This extends a result of Gueritaud-Kassel-Wolff to the case of $\mathrm{PSL}_2 (\mathbb{C})$-representations. Our proof involves straightening the pleated plane in $\mathbb{H}^3$ determined by the Fock-Goncharov coordinates of a framed representation, and applying strip-deformations.
