Primitive Homology Representation Of Finite Graph Covers

Abstract

Given a cover of a graph ρ : Y → X with associated deck group transformation G, we provide its first homology as a G−representation. We introduce the concept of primitive homology H prim 1 (Y ; C) ⊂ (Y ; C) and provide some results about the cases when H prim 1 (Y ; C) = H1(Y ; C). For example abelian covers. We then end in an example fo a group for which the equality doesn’t hold.