# Contractibility  of the space of tight contact structures on ${\mathbb R}^3$

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Yasha Eliashberg, Stanford University/IAS
IAS - Simonyi Hall Seminar Room SH-101

In-Person Talk

30 years ago I proved that any tight contact structure on the 3-sphere is diffeomorphic to the standard one. I also optimistically claimed at the same  paper  that similar methods could be used to prove a multi-parametric version: the space of tight contact structures on  the 3-sphere, fixed at a point, is contractible. In our recent joint with N. Mishachev paper we proved this result. While the proof indeed roughly follows the strategy of my 1991 paper, it is much more involved. In particular, it uses a new criterion for tightness of of a characteristic foliation on the 2-sphere, which is valid without any contact  convexity assumptions.