论文标题
希格斯束，谐波图和百褶表面
Higgs bundles, harmonic maps, and pleated surfaces
论文作者
论文摘要
本文将表面组的SL（2，c）表示的特征品种的渐近几何形状结合了量规理论和双曲几何观点。具体而言，我们在分析定义定义的限制配置之间找到了su（2）自偶性方程的分析定义的限制配置，这是由Mazzeo-Swoboda-weiss-Weiss-Weiss-witt构建的封闭的riemann表面，以及在超纤维三范围内造成超级纤维三 - 散布的几何形状拓扑参数和造型的几何形状拓扑参数。几何链接来自非亚伯杂货的对应关系和谐波图的高能量变性的研究。我们的结果有多个应用程序。我们证明：（1）通过限制配置，将解决方案模量空间的部分压实局部压实的局部不变性； （2）对角色品种摩根 - 沙伦紧凑型的谐波图表的改进； （3）由二次差分定义的复杂投影结构的家族与相应平坦连接的实现为希格斯捆绑包，并确定了瑟斯顿褶皱表面的渐近剪切弯曲旋转酶的确定。
This paper unites the gauge-theoretic and hyperbolic-geometric perspectives on the asymptotic geometry of the character variety of SL(2,C) representations of a surface group. Specifically, we find an asymptotic correspondence between the analytically defined limiting configuration of a sequence of solutions to the SU(2) self-duality equations on a closed Riemann surface constructed by Mazzeo-Swoboda-Weiss-Witt, and the geometric topological shear-bend parameters of equivariant pleated surfaces in hyperbolic three-space due to Bonahon and Thurston. The geometric link comes from the nonabelian Hodge correspondence and a study of high energy degenerations of harmonic maps. Our result has several applications. We prove: (1) the local invariance of the partial compactification of the moduli space of solutions to the self-duality equations by limiting configurations; (2) a refinement of the harmonic maps characterization of the Morgan-Shalen compactification of the character variety; and (3) a comparison between the family of complex projective structures defined by a quadratic differential and the realizations of the corresponding flat connections as Higgs bundles, as well as a determination of the asymptotic shear-bend cocycle of Thurston's pleated surface.
