國立清華大學 數學系

Abstract:
In this talk, we will consider path cohomology groups of digraphs (i.e. directed graphs) as Brown functors. We will start with a homology theory for digraphs, and we will show that this homology is a homotopy invariant. The cohomology groups for digraphs can be obtained by taking the dual of the path chain complexes. We then show that the zeroth and the first path cohomology groups for finite directed graphs are the Brown functors, that is, they satisfy the Additivity axiom and the Mayer-Vietoris axiom.