Completing Prelaminations

Thomas Barthelmé; Christian Bonatti; Kathryn Mann

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arXiv · 2406.18917

Completing Prelaminations

Thomas Barthelmé·Christian Bonatti·Kathryn Mann

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Abstract

Motivated by problems in the study of Anosov and pseudo-Anosov flows on 3-manifolds, we characterize when a pair $(L^+, L^-)$ of subsets of transverse laminations of the circle can be completed to a pair of transverse foliations of the plane or, separately, realized as the endpoints of such a bifoliation of the plane. (We allow also singular bifoliations with simple prongs, such as arise in pseudo-Anosov flows). This program is carried out at a level of generality applicable to bifoliations coming from pseudo-Anosov flows with and without perfect fits, as well as many other examples, and is natural with respect to group actions preserving these structures.

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Thomas Barthelmé, Christian Bonatti, Kathryn Mann. 2024-06-27. Completing Prelaminations. https://arxiv.org/abs/2406.18917

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