O’Uchi, Moto Coverings of foliations and associated \(C^*\)-algebras. (English) Zbl 0598.58032 Math. Scand. 58, 69-76 (1986). Let \((V,F)\) and \((V',F')\) be \(C^{\infty}\) foliations with the associated \(C^*\)-algebras \(C^*(V,F)\) and \(C^*(V',F')\). The author introduces the notion of homogeneous covering map of \((V,F)\) onto \((V',F')\) with the structure group \(Z\). Then it is shown that such a map determines an action \(\beta\) of \(Z\) on \(C^*(V,F)\) such that the reduced crossed product of \(C^*(V,F)\) by \(\beta\) is isomorphic to \(C^*(V',F')\). This result is applied for studying two Anosov foliations. Reviewer: Dumitru Motreanu (Perpignan) Cited in 1 Document MSC: 37C85 Dynamics induced by group actions other than \(\mathbb{Z}\) and \(\mathbb{R}\), and \(\mathbb{C}\) 57R30 Foliations in differential topology; geometric theory 57S25 Groups acting on specific manifolds 46L35 Classifications of \(C^*\)-algebras 46L40 Automorphisms of selfadjoint operator algebras Keywords:smooth manifold; transverse submanifold; holonomy groupoid; action of a group; \(C^*\)-algebras; homogeneous covering map; crossed product; Anosov foliations PDF BibTeX XML Cite \textit{M. O'Uchi}, Math. Scand. 58, 69--76 (1986; Zbl 0598.58032) Full Text: DOI EuDML OpenURL