Nov 15

Title: Left orderability and taut foliations with one-sided branching

Speaker: Bojun Zhao (University at Buffalo)

Abstract: Let M be a closed orientable irreducible 3-manifold. We will talk about some results to show that π1(M) is left orderable in the following cases:

(1) Suppose that M admits a co-orientable taut foliation with one-sided branching, then π1(M) is left orderable.

(2) Suppose that M admits a co-orientable taut foliation with orderable cataclysm, then π1(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 π1(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 π1(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.