BIMSA > Group Meeting on Algebraic Topology and Its Applications Calculating higher digraph homotopy groups
Calculating higher digraph homotopy groups
Organizers
Feng Chun Lei , Jing Yan Li , Yang Yang Ruan , Jie Wu
Speaker
Meng Meng Zhang
Time
Wednesday, May 7, 2025 1:00 PM - 2:00 PM
Venue
A3-1a-205
Online
Zoom 435 529 7909 (BIMSA)
Abstract
In 2014, Grigor’yan, Lin, Muranov and Yau introduced the homotopy theory of digraphs and defined the digraph homotopy groups by taking the fundamental group of the (n-1)-fold iterated based loop digraph. Then inspired by the cubical approach to defining the higher homotopy groups of a based space, a more direct approach to defining higher digraph homotopy groups, which exhibit properties similar to those of the homotopy groups of based topological spaces, was given. At this point two questions naturally arise. Is there a digraph whose higher homotopy group is nontrivial? What other properties of higher homotopy groups for topological spaces have digraph analogues? The purpose of this paper is to address these questions. This is joint work with Stephen Theriault, Jie Wu, and Shing-Tung Yau.