# Mathematics Colloquia and Seminars

### Taut foliations from left orders in Heegaard genus 2.

Geometry/Topology

 Speaker: Sarah Rasmussen, Cambridge and IAS Related Webpage: https://www.dpmms.cam.ac.uk/~sr727/ Location: Zoom Start time: Tue, Oct 13 2020, 1:10PM

Until now, taut foliations on hyperbolic 3-manifolds have generally only been constructed using branched surfaces, whether via sutured manifold hierarchies, spanning surfaces of knot exteriors, or Dunfield's one-vertex triangulations with foliar orientations. I now have a novel taut foliation construction that makes no recourse to branched surfaces. Instead, it starts with a transversely-foliated $\mathbb{R}$-bundle over a Heegaard surface, specified by a real line action from a left-invariant order on the fundamental group of the 3-manifold. Relating taut foliations to fundamental group left orders is an old question that interested Thurston, Gabai, and Calegari, and has been revived in recent years by the L-space conjecture. This construction works reliably for genus 2 Heegaard diagrams satisfying mild conditions, explaining numerical results of Dunfield.