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Title:
Contractibility of the space of tight contact structures on R^3
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Abstract:
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 a characteristic foliation on the 2-sphere, which is valid without any contact convexity assumptions.
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