Bojun Zhao (UQAM)

Title: R-covered foliations, left-orderability, and Dehn fillings

Abstract: Surface fibrations give the simplest examples of taut foliations of 3-manifolds. In the universal cover, the lifted fibers are naturally parametrized by a real line. An R-covered foliation retains this global picture: roughly speaking, its leaves can still be globally parametrized by R, even though the manifold itself need not fiber over the circle. Known constructions of R-covered foliations typically arise from a few special geometric or dynamical settings.

The L-space conjecture predicts that a closed irreducible 3-manifold admits a co-orientable taut foliation if and only if its fundamental group is left-orderable. In this context, an R-covered foliation is not only a particularly simple form of taut foliation, but also provides a direct dynamical realization of left-orderability.

I will discuss pseudo-Anosov mapping tori whose stable foliations are co-orientable but whose monodromies reverse the co-orientation. We show that Dehn fillings with slopes outside a certain neighborhood of the degeneracy slope admit R-covered foliations. Combined with earlier work, this verifies the L-space conjecture for all surgeries on the (-2,3,2q+1)-pretzel knots in S^3, for q at least 3.

No prior knowledge of foliation theory will be assumed in this talk.

We will have tea after the talk in the grad lounge and play some board games at 5pm.