BIMSA > BIMSA Topology Seminar BIMSA Topology Seminar Digraph Spheres and Homotopy Groups of Digraphs
Digraph Spheres and Homotopy Groups of Digraphs
Organizers
Jingyan Li , Pravin Kumar , Jie Wu
Speaker
Jingyan Li
Time
Thursday, November 26, 2026 3:00 PM - 4:00 PM
Venue
A3-4-301
Online
Zoom 242 742 6089 (BIMSA)
Abstract
We study higher homotopy groups of digraphs defined by based maps from digraph spheres and compare them with the original GLMY homotopy groups defined recursively using loop digraphs. The two theories agree in dimension one, but they can differ in higher dimensions. We exhibit a six-vertex digraph for which the original GLMY second homotopy group is trivial, while the sphere-based second homotopy group contains an element of infinite order. This element is detected by a natural Hurewicz homomorphism to GLMY path homology with integer coefficients. We then introduce a pointwise-tail loop digraph and prove that it gives a natural recursion for the sphere homotopy groups.
Speaker 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.