Rachel Hardeman

Title: An Introduction to A-Homotopy Theory: A Discrete Homotopy Theory for Graphs
Abstract:
A-homotopy Theory was invented by Ron Aktin in the 1970s and further developed by Helene Barcelo in the early 2000s as a combinatorial version of homotopy theory. This theory respects the structure of a graph, distinguishing between vertices and edges. While in classical homotopy theory all cycles are equivalent to the circle, in A-homotopy theory the 3 and 4-cycles are contractible and all larger cycles are equivalent to the circle.
In this talk, we will examine the fundamental group in A-homotopy from the perspective of covering spaces. We will also establish explicit lifting criteria and examine the role of the 3 and 4-cycles in these criteria.