Equivalent curves on surfaces

Abstract

We consider a closed oriented surface of genus at least 2. To describe curves on it, one natural idea is to choose once for all a collection of curves as a reference system and to hope that any other curve can be determined by its intersection numbers with reference curves. For simple curves, using the work of Dehn and Thurston, it is possible to find such a reference system consisting of finitely many simple curves. The situation becomes more complicated when curves have self-intersections. In particular, for any non negative integer k, it is possible to find a pair of curves having the same intersection number with every curve with k self-intersections. Such a pair of curves are called k-equivalent curves. In this talk, I will discuss the general picture of a pair of k-equivalent curves and the relation between k-equivalence relations for different k's. This is a joint-work with Hugo Parlier.

Speaker

徐彬斌，南开大学数学科学学院副教授。2008年毕业于清华大学数学与应用数学专业。2011年在法国格勒诺布尔一大获得基础数学硕士学位，2014年在法国格勒诺布尔阿尔卑斯大学获得数学博士学位。研究领域：几何拓扑。

个人主页：

https://my.nankai.edu.cn/sms/xbb/list.htm