Abstract. We compute zeta functions of 1-solenoids. When our 1-solenoid is nonorientable, we compute Artin-Mazur zeta function and Lefschetz zeta function of the 1-solenoid and its orientable double cover explicitly in terms of adjacency matrices and branch points. And we show that Artin-Mazur zeta function of orientable double cover is a rational function and a quotient of Artin-Mazur zeta function and Lefschetz zeta function of the 1-solenoid.

For a locally compact higher rank graph Λ, we construct a two-sided path space Λ ∆ with shift homeomorphism σ and its corresponding path groupoid Γ. Then we find equivalent conditions of aperiodicity, cofinality and irreducibility of Λ in (Λ ∆ , σ), Γ, and the groupoid algebra C * (Γ).