Margulis spacetimes via the arc complex
Margulis spacetimes via the arc complex
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DOI：
10.1007/s00222-015-0610-z
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发表时间：
2014-07
影响因子：
3.1
通讯作者：
J. Danciger;François Guéritaud;Fanny Kassel
中科院分区：
文献类型：
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作者：
J. Danciger;François Guéritaud;Fanny Kassel
我们研究凸余紧双曲曲面的条形变形，其定义是沿着适当嵌入曲面的一组不相交的测地线弧线插入双曲条带。证明了均匀拉长所有闭测地线的曲面的任何变形都可以以一种本质上唯一的方式实现为条形变形。这一结果的无穷小版本给出了具有固定凸余紧线性完整系统的Marguis时空模空间的弧复形化。作为应用，我们通过建立弯曲平面猜想，给出了这类Marguis时空平稳性的一个新的证明。该猜想指出，构成一个由分段线性曲面限定的基本区域，称为弯曲平面。非无穷小版本给出了非紧致完备反de Sitter 3-流形的类似理论。
We studystrip deformationsof convex cocompact hyperbolic surfaces, defined by inserting hyperbolic strips along a collection of disjoint geodesic arcs properly embedded in the surface. We prove that any deformation of the surface that uniformly lengthens all closed geodesics can be realized as a strip deformation, in an essentially unique way. The infinitesimal version of this result gives a parameterization, by the arc complex, of the moduli space of Margulis spacetimes with fixed convex cocompact linear holonomy. As an application, we provide a new proof of the tameness of such Margulis spacetimesMby establishing the Crooked Plane Conjecture, which states thatMadmits a fundamental domain bounded by piecewise linear surfaces called crooked planes. The noninfinitesimal version gives an analogous theory for noncompact complete anti-de Sitter 3-manifolds.