论文标题
用于负弯曲表面的Teichmuller空间
A Teichmuller space for negatively curved surfaces
论文作者
论文摘要
我们首先描述了可变负曲率的封闭表面的基本组在其通用覆盖中的定向地理学上的基本组，其自然定义平坦的连接在于，其自达性在于，汉密尔顿二型的差异性s^1 x x x R.对整体的考虑。对整体的考虑需要从riemannian from riemannian from riemannian from from riemannian from from riemannian from versler merics forsler merics forsler forsler merics。本文的第二部分遵循Higgs束方法，以适应该无限尺寸群体的平坦连接，并依靠O.Biquard的构造，专注于一个指标家族，该构建由CR函数的无限二维空间参数化。这生成了定义连接的替代方法，并提供了代表模量空间的媒介空间的可能性，该空间概括并包括经典的Teichmueller空间。
We first describe the action of the fundamental group of a closed surface of variable negative curvature on the oriented geodesics in its universal covering in terms of a naturally-defined flat connection whose holonomy lies in the group of Hamiltonian diffeomorphisms of S^1 x R. Consideration of the holonomy necessitates an extension from Riemannian to Finsler metrics. The second part of the paper follows the Higgs bundle approach to flat connections adapted to this infinite dimensional group and focuses on a family of metrics, relying on a construction of O.Biquard, which is parametrized by the infinite-dimensional space of CR functions on the unit circle bundle of a hyperbolic surface. This generates an alternative approach to defining a connection and offers the possibility of this vector space representing a moduli space which generalizes and includes the classical Teichmueller space.
