## 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)×r 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:E ^{1} → G. The group acts freely and properly on this new topological graph EA - c G. If G is abelian, there is a dual action on C ^{*} (E) such that $C*(E) {G}\cong C*(E×cG)$. We also define the fundamental group and the universal covering of a topological graph.

Original language | English (US) |
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Pages (from-to) | 1527-1566 |

Number of pages | 40 |

Journal | Ergodic Theory and Dynamical Systems |

Volume | 32 |

Issue number | 5 |

DOIs | |

State | Published - Oct 1 2012 |

## ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics