Homotopy covers of graphs
Laura Scull (scull_l@fortlewis.edu)
We develop a theory of ×-homotopy, fundamental groupoids and covering spaces that applies to non-simple graphs, generalizing existing results for simple graphs. We prove that ×-homotopies from finite graphs can be decomposed into moves that adjust at most one vertex at a time, generalizing the spider lemma of Chih & Scull (2021). We define a notion of homotopy covering map and develop a theory of universal covers and deck transformations, generalizing Matsushita (2017) and Tardif–Wroncha (2019)