Seminar

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This is the continuation of the talk of Rafael Potrie last week. We showed with him in https://arxiv.org/abs/2510.15176  that a pair of transverse foliations by Gromov hyperbolic leaves in a closed 3-manifold either intersects in a leafwise quasigeodesic manner, or it contains a (generalized) Reeb surface. I will talk about the case that if L, E are leaves of the two foliations in the universal cover, then their intersection is connected, that is a single bi-infinite properly embedded arc. This part of the proof at this point needs that leaves are Gromov hyperbolic. The analysis is pretty much independent of part 1, which did not need Gromov hyperbolicity at all, and part 2 uses much more geometric ideas.

Translation: you can still understand most of it if you missed part 1.