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

Ya. M. Ehliashberg, Nikolai Mishachev

Publication date: 21 August 2021

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.

Mathematics Subject Classification ID

Symplectic manifolds (general theory) (53D05) Global theory of symplectic and contact manifolds (53D35) Contact manifolds (general theory) (53D10)

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