Immersions and the space of all translation structures
Immersions and the space of all translation structures
复制标题
沉浸感和所有翻译结构的空间
DOI：
--
复制
发表时间：
2013
期刊：
影响因子：
--
通讯作者：
W. Hooper
中科院分区：
文献类型：
--
作者：
W. Hooper
表面上的平移结构是图表到平面的图谱，因此过渡函数是平移。我们允许曲面是非紧的和无限亏格的。我们赋予空间的所有点的表面配备了一个平移结构的拓扑结构，我们称之为沉浸式拓扑，因为它是有关的方式，其中磁盘可以沉浸到这样的表面。我们证明了一些操作通常做平移表面是连续的拓扑结构。我们表明，拓扑是豪斯多夫，并收集表面上的一个固定的下界的内射半径在基点是紧凑的。
A translation structure on a surface is an atlas of charts to the plane so that the transition functions are translations. We allow our surfaces to be non-compact and infinite genus. We endow the space of all pointed surfaces equipped with a translation structure with a topology, which we call the immersive topology because it is related to the manner in which disks can be immersed into such a surface. We prove that a number of operations typically done to translation surfaces are continuous with respect to the topology. We show that the topology is Hausdorff, and that the collection of surfaces with a fixed lower bound on the injectivity radius at the basepoint is compact.