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It was proven in the first author's paper "Contact 3-manifolds twenty yearssince J. Martinet's work" (Ann. Inst. Fourier, 42(1992), 165--192) that anytight 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 toprove 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 currentpaper.

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