李京艳 , 普拉文·库马尔 , 吴杰

李京艳

2026年11月26日 15:00 至 16:00

A3-4-301

Zoom 242 742 6089 (BIMSA)

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.

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。