AbstractThe past decade has seen large literatures develop around two novel invariants of directedgraphs: magnitude homology (due to Leinster, Hepworth and Wilerton) and the path homology ofGLMY theory. Though their origins are quite separate, Asao proved in 2022 that in fact thesehomology theories are intimately related. To every directed graph one can associate a certainspectral sequence - th...
AbstractWe discuss the notions of path homology and homotopy of digraphs. The following topic will bepresented.. Homology groups of digraphs.. Homotopy of digraph maps and digraphs. lnvariance of homology groups under homotopy.Fundamental group of a digraph. Invariance of the fundamental group under homotopy.Relation between the fundamental group and first homology group.Speaker IntroProfessor ...