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Uniform 1-cochains and genuine laminations. (English) Zbl 1151.57018

Summary: We construct a pair of transverse genuine laminations on an atoroidal 3-manifold admitting a transversely orientable uniform 1-cochain. The laminations are induced by the uniform 1-cochain and they are the straightening of the coarse laminations defined by Calegari, by using minimal surface techniques. Moreover, when we collapse these laminations, we get a topological pseudo-Anosov flow, as defined by Mosher.

MSC:

57M50 General geometric structures on low-dimensional manifolds
57N10 Topology of general \(3\)-manifolds (MSC2010)