Group actions on topological graphs

Abstract. We define the action of a locally compact group G on a topological graph E. This action induces a natural action of G on the C∗-correspondence H(E) and on the graph C∗-algebra C∗(E). If the action is free and proper, we prove that C∗(E) or G is strongly Morita equivalent to C∗(E/G). We define the skew product of a locally compact group G by a topological graph E via a cocycle c: E1 → G. The group acts freely and properly on this new topological graph E ×c G. If G is abelian, there is a dual action on C∗(E) such that C∗(E) o G ̂ ∼ = C∗(E ×c G). We also define the fundamental group and the universal covering of a topological graph. 1