三维时空模空间上的广义剪切坐标
Generalised shear coordinates on the moduli spaces of three-dimensional spacetimes
摘要：
在具有尖点Cauchy曲面S的极大整体双曲常曲率三维时空的模空间上引入坐标。它们是由S的Teichmüller空间上的测地线层丛对模空间的参数化导出的，可以看作是Teichmüller空间上剪切坐标的解析延拓。在这些坐标下，引力辛结构具有特别简单的形式，类似于剪切坐标下的Weil-Petersson辛结构，并且与Teichmüller空间的余切丛密切相关。然后，我们考虑映射类群作用在模空间上，并证明它保持引力辛结构。这定义了Teichmüller空间余切丛上的三个不同的映射类群作用，对应于不同的曲率值。
英文摘要：
We introduce coordinates on the moduli spaces of maximal globally hyperbolic constant curvature 3d spacetimes with cusped Cauchy surfaces S. They are derived from the parametrisation of the moduli spaces by the bundle of measured geodesic laminations over Teichmüller space of S and can be viewed as analytic continuations of the shear coordinates on Teichmüller space. In terms of these coordinates the gravitational symplectic structure takes a particularly simple form, which resembles the Weil-Petersson symplectic structure in shear coordinates, and is closely related to the cotangent bundle of Teichmüller space. We then consider the mapping class group action on the moduli spaces and show that it preserves the gravitational symplectic structure. This defines three distinct mapping class group actions on the cotangent bundle of Teichmüller space, corresponding to different values of the curvature.
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