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.


57R30 Foliations in differential topology; geometric theory
57N10 Topology of general \(3\)-manifolds (MSC2010)
57M50 General geometric structures on low-dimensional manifolds
Full Text: DOI


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