**Date/Time**

Date(s) - 09/03/2023*3:30 pm - 4:30 pm*

Name: Bojun Zhao, University at Buffalo

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

**Abstract:** Let M be a closed orientable irreducible 3-manifold that admits aco-orientable taut foliation F. We provide some results to show that ?_1(M) isleft orderable in the following cases:

(1) Suppose that M admits a co-orientable taut foliation with one-sidedbranching, then ?_1(M) is left orderable.

(2) Suppose that M admits a co-orientable taut foliation with orderablecataclysm, then ?_1(M) is left orderable. We give some examples of tautfoliations with this property:

2-a: If a co-orientable taut foliation F is the stable foliation of anAnosov flow, then F has orderable cataclysm. In this case, it’s known that ?_1(M) is left orderable by lifting Thurston’s universal circle action throughthe Euler class, from the works of Thurston, Calegari-Dunfield, Boyer-Hu andBoyer-Rolfsen-Wiest. Our result gives a new proof, and the left-invariant orderof ?_1(M) comes from a different way.

2-b: Assume that a pseudo-Anosov flow has co-orientable stable singularfoliation. Then there are infinitely many closed 3-manifolds obtained from Dehnfilling over the union of singular orbits that admit co-orientable tautfoliations with orderable cataclysm.

**Venue:** online and live streamed in HH-312