Geometry & Topology Seminar-Bojun Zhao-Left orderability and taut foliations with one-sided branching
Mar 9, 2023
3:30PM to 4:30PM
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