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arXiv · 2108.09452

The space of tight contact structures on ${\mathbb R}^3$ is contractible

Yakov Eliashberg·Nikolai Mishachev
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Abstract

It was proven in the first author's paper "Contact 3-manifolds twenty years since J. Martinet's work" (Ann. Inst. Fourier, 42(1992), 165--192) that any tight contact structure on the 3-sphere is diffeomorphic to the standard one. It was also claimed there without a proof that similar methods could be used to prove a multi-parametric version: the space of tight contact structures on $S^3$, fixed at a point, is contractible. We prove this result in the current paper.

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Yakov Eliashberg, Nikolai Mishachev. 2021-08-21. The space of tight contact structures on ${\mathbb R}^3$ is contractible. https://arxiv.org/abs/2108.09452

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