Finite covers of graphs, their primitive homology, and representation theory.

Consider a finite, regular cover Y → X of finite graphs, with associated deck group G. We relate the topology of the cover to the structure of H1(Y;ℂ) as a G-representation. A central object in this study is the primitive homology group Hprim1 (Y;ℂ) ⊆ H1(Y ;ℂ), which is the span of homology classes represented by components of lifts of primitive elements of π1(X). This circle of ideas relates combinatorial group theory, surface topology, and representation theory. [ABSTRACT FROM AUTHOR]