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Feb 27, 2021 at 22:04 comment added Douglas Finamore Yes, by a transversal I mean a submanifold whose dimension is the same as the codimension of the foliation. I'm also assuming the ambient manifold is closed, otherwise there could be taut foliations without closed transversals, even in codimension one.
Feb 27, 2021 at 21:36 comment added Mehdi Yazdi Suppose the foliation has codimension k. Should the transversal that you are asking for have codimension k as well? If yes then there are multiple possibilities for the topology of a transversal.
Feb 17, 2021 at 20:52 history asked Douglas Finamore CC BY-SA 4.0