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Modifying a branched surface to carry a foliation. (English) Zbl 1143.57014
The authors deal with the problem of existence of transverse foliations for non-singular flows on closed 3-manifolds. They prove for a Reebless flow that it is transverse to a foliation F if and only if its associated branched transverse surface can be modified to carry F while staying transverse to the flow.

MSC:
57R30Foliations; geometric theory (differential topology)
57N10Topology of general 3-manifolds
57M50Geometric structures on low-dimensional manifolds