走向现代数学学术报告 - 赵学志教授（No. 575）

报告题目：A generalization of degree and its applications in knot theory

报告人：赵学志 教授（首都师范大学）

报告时间：2023年2月27日 14:00

腾讯会议ID：226349906

报告摘要：Given a map $f: X\to Y$, the local degree of $f$ at a point $y_0$ is an algebraic counting of the number of points in $f^{-1}(y_0)$. By using homological theory, we consider more general situation and give some invariants to describe the set of $f^{-1}(B)$, where $B$ is a non-empty closed subset of $Y$. A lower bound for the number of components $f^{-1}(B)$ will be explained. We shall illustrate how to use this generalized degree  to obtain some invariants for knots and links.

References

Ying Gu, Xuezhi Zhao,  Common value pairs and their estimations. Bull. Belg. Math. Soc. Simon Stevin 24 (2017), no. 4, 725--739.

Xing Chen, Xuezhi Zhao, Knot invariants coming from pre-image indices, Topological Methods in Nonlinear Analysis, 56(2020), no. 2, 519--528.

报告人简介：赵学志，首都师范大学数学科学学院教授，博士生导师。博士毕业于北京大学，在基础数学中的研究方向为代数拓扑学，研究内容包括拓扑不动点理论，三维流形上的动力系统，李群及相关空间的拓扑结构等。