Homotopy of (di)graphs and quivers II
In this course, we introduce some basic methods of algebraic topology in graph theory. We mainly fcus on the homotopy theory of (di)graphs and quivers, we will introduce the fundamental group and the higher dimensional homotopy groups of (di)graphs and some of the properties.
讲师
日期
2025年03月25日 至 05月20日
位置
| Weekday | Time | Venue | Online | ID | Password |
|---|---|---|---|---|---|
| 周二,周四 | 08:50 - 11:25 | A3-4-301 | ZOOM 08 | 787 662 9899 | BIMSA |
修课要求
Basic notions of algebra and topology
课程大纲
Chapter 1. Categories of digraphs, graphs, and quivers.
Chapter 2. Homotopy in the graph theory.
Chapter 3. $\pi_0(G)$ of a digraph.
Chapter 4. The fundamental group $\pi_1(G)$.
Chapter 5. The properties of $\pi_1(G)$ .
Chapter 6. The strong product $\boxtimes$ of digraphs.
Chapter 7. Applications of fundamental groups to graph coloring and the fundamental groupoid in the category of graphs.
Chapter 8. Higher dimensional homotopy groups of (di)graphs.
Chapter 2. Homotopy in the graph theory.
Chapter 3. $\pi_0(G)$ of a digraph.
Chapter 4. The fundamental group $\pi_1(G)$.
Chapter 5. The properties of $\pi_1(G)$ .
Chapter 6. The strong product $\boxtimes$ of digraphs.
Chapter 7. Applications of fundamental groups to graph coloring and the fundamental groupoid in the category of graphs.
Chapter 8. Higher dimensional homotopy groups of (di)graphs.
参考资料
[1] Grigor’yan, A., Lin, Y., Muranov, Y., Yau, S.-T., Homologies of path complexes and digraphs, arXiv: 1207.2834v4, 2012. GLMY Grigor’yan, A., Lin, Y., Muranov, Y., Yau, S.-T., Path complexes and their homologies, J. Math. Sciences, 248, 2020, 564-599.
[2] Grigor’yan, A., Lin, Y., Muranov, Y., Yau, S.-T., Homotopy Theory for Digraphs, Pure Appl. Math. Q., 10(4), 2015, 619-674.
[3] Mac Lane, S., Categories for the working mathematician, Springer Science & Business Media, Vol. 5, 2013.
[4] Maunder, C. R. F., Algebraic topology, Courier Corporation, 1996.
[5] Puppe, D., Homotopiemengen und ihre induzierten Abbildungen, I. Mathematische Zeitschrift, 69(1), 1958, 299-344.
[6] Jingyan Li, Jie Wu, Shing-Tung Yau, Mengmeng Zhang, Homotopy Groups and Puppe Sequence of Digraphs, Preprint.
[2] Grigor’yan, A., Lin, Y., Muranov, Y., Yau, S.-T., Homotopy Theory for Digraphs, Pure Appl. Math. Q., 10(4), 2015, 619-674.
[3] Mac Lane, S., Categories for the working mathematician, Springer Science & Business Media, Vol. 5, 2013.
[4] Maunder, C. R. F., Algebraic topology, Courier Corporation, 1996.
[5] Puppe, D., Homotopiemengen und ihre induzierten Abbildungen, I. Mathematische Zeitschrift, 69(1), 1958, 299-344.
[6] Jingyan Li, Jie Wu, Shing-Tung Yau, Mengmeng Zhang, Homotopy Groups and Puppe Sequence of Digraphs, Preprint.
听众
Undergraduate
, Graduate
视频公开
不公开
笔记公开
不公开
语言
中文
讲师介绍
李京艳，BIMSA助理研究员，2007年获河北师范大学数学系博士学位，先后执教于石家庄铁道大学数理系和河北师范大学数学科学学院，职称副教授，2021年9月入职北京雁栖湖应用数学研究院（BIMSA）。主要研究兴趣在拓扑数据分析和单纯同调与同伦方面。