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Topology/Geometry Seminar

Left orderability and taut foliations with one-sided branching

Bojun Zhao (University at Buffalo)

Location:  Hill Center, Room 705
Date & time: Tuesday, 15 November 2022 at 4:00PM - 5:00PM

Let M be a closed orientable irreducible 3-manifold. We will talk about some results to show that \(\pi_1(M)\) is left orderable in the following cases:
(1) Suppose that M admits a co-orientable taut foliation with one-sided branching, then \(\pi_1(M)\) is left orderable.
(2) Suppose that M admits a co-orientable taut foliation with orderable cataclysm, then \(\pi_1(M)\) is left orderable. We give some examples of taut foliations with this property:
2-a: If an Anosov flow has co-orientable stable and unstable foliations, then the stable and unstable foliations have orderable cataclysm. In this case, it’s known that \(\pi_1(M)\) is left orderable by combining the works of Thurston, Calegari-Dunfield, Boyer-Hu and Boyer-Rolfsen-Wiest. Our result gives a new proof, and the left-invariant order of \(\pi_1(M)\) comes from a different way.
2-b: Assume that a pseudo-Anosov flow has co-orientable stable and unstable singular foliations, and the stabilizer at every singular orbit does not rotate the prongs, then the resulting foliation obtained from splitting the stable singular foliation and filling with monkey saddles has orderable cataclysm.

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