Taut foliations, contact structures, and the L-space conjecture

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Thomas Massoni, Princeton University
Fine Hall 314

In the late '90s, Eliashberg and Thurston established a remarkable connection between foliations and contact structures in dimension three: 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 present a converse result concerning the construction of taut foliations from suitable pairs of contact structures. I will also describe a comprehensive dictionary between the languages of foliations and of (pairs of) contact structures. 

Although taut foliations are usually considered rigid objects, this contact viewpoint reveals some degree of flexibility. It also provides a new insight on the celebrated L-space conjecture. I will discuss some results in this direction and speculate about potential future directions.