Wild translation surfaces and infinite genus
Wild translation surfaces and infinite genus
复制标题
狂野的平移表面和无限的属
DOI：
10.2140/agt.2018.18.2661
复制
发表时间：
2014
影响因子：
0.7
通讯作者：
Anja Randecker
中科院分区：
文献类型：
--
作者：
Anja Randecker
经典平移曲面的Gauss-Bonnet公式将奇点(几何)的锥角与曲面(拓扑)的亏格联系起来。当考虑更一般的平移面时，我们观察到所谓的野生奇点，圆锥角的概念不再适用于这些奇点。我们研究了具有野奇性的平移曲面的几何和拓扑之间是否仍然存在关系。通过考虑短鞍点连接，我们确定在什么条件下，野奇点的存在蕴含无限亏格。应用这一点，我们证明了具有野生奇点的抛物线平移曲面或本质有限平移曲面有无限亏格。
The Gauss-Bonnet formula for classical translation surfaces relates the cone angle of the singularities (geometry) to the genus of the surface (topology). When considering more general translation surfaces, we observe so-called wild singularities for which the notion of cone angle is not applicable any more. We study whether there still exist relations between the geometry and the topology for translation surfaces with wild singularities. By considering short saddle connections, we determine under which conditions the existence of a wild singularity implies infinite genus. We apply this to show that parabolic or essentially finite translation surfaces with wild singularities have infinite genus.