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.
Lecturer
Date
25th March ~ 20th May, 2025
Location
| Weekday | Time | Venue | Online | ID | Password |
|---|---|---|---|---|---|
| Tuesday,Thursday | 08:50 - 11:25 | A3-4-301 | ZOOM 08 | 787 662 9899 | BIMSA |
Prerequisite
Basic notions of algebra and topology
Syllabus
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.
Reference
[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.
Audience
Undergraduate
, Graduate
Video Public
No
Notes Public
No
Language
Chinese
Lecturer Intro
Assistant Reserch fellow Jingyan Li received a PhD degree from the Department of Mathematics of Hebei Normal University in 2007. Before joining BIMSA in September 2021, she has taught in the Department of Mathematics and Physics of Shijiazhuang Railway University and the School of Mathematical Sciences of Hebei Normal University as an associate professor. Her research interests include topology data analysis and simplicial homology and homotopy.