Taut foliations through a contact lens

Thomas Massoni, Princeton University
Fine Hall 314

In-Person Talk 

In the late 90s, Eliashberg and Thurston proved that any cooriented foliation on a closed, oriented $3$-manifold different from $S^1 \times S^2$ can be approximated by positive and negative contact structures. If the foliation is taut, then its contact approximations are (universally) tight.

In this talk, I will explain how to construct foliations from suitable pairs of contact structures and describe a dictionary between the language of foliations and the language of contact pairs. Taut foliations are rather rigid objects by nature; from this contact viewpoint, they acquire some flexibility. As an application of this principle, I will show that taut foliations survive after performing large slope surgeries on transverse knots.