Taut foliations from knot diagrams
1 : University of Wien
Taut foliations have been a classical object of study in 3-manifolds theory. Recently, new interest in them has come from the investigation of the so-called "L-space conjecture", that predicts that Heegaard Floer L-spaces can be characterised as those 3-manifolds that do not admit coorientable taut foliations. A possible approach to the study of this conjecture is by analysing surgeries on knots and links. Most of the techniques employed for constructing taut foliations on Dehn surgeries usually make use of some special property of the exterior of the link (e.g. fiberedness). In this talk I will provide a diagrammatic condition which implies the existence of taut foliations on all non-trivial surgeries on a knot.