Geometric intersection in representations of mapping class groups of surfaces
Geometric intersection in representations of mapping class groups of surfaces
复制标题
曲面映射类组表示中的几何交集
DOI：
10.1016/j.topol.2016.12.005
复制
发表时间：
2017
影响因子：
0.6
通讯作者：
Yasushi Kasahara
中科院分区：
文献类型：
--
作者：
Anton Ayzenberg;Mikiya Masuda;Mikiya Masuda;Mikiya Masuda;Mikiya Masuda;Mikiya Masuda;Mikiya Masuda;Mikiya Masuda;Mikiya Masuda;Yasushi Kasahara
我们证明了在曲面的映射类群的任意表示中检测几何相交意味着该表示到中心的注入性，反之亦然。作为应用，我们讨论了约翰逊滤波中的几何相交问题。此外，我们还进一步研究了在一个表示中分离的简单封闭曲线之间的几何相交的检测问题。
We show that the detection of geometric intersection in an arbitrary representation of the mapping class group of surface implies the injectivity of that representation up to center, and vice versa. As an application, we discuss the geometric intersection in the Johnson filtration. Also, we further consider the problem of detecting the geometric intersection between separating simple closed curves in a representation.