The space of tight contact structures on ${\mathbb R}^3$ is contractible
Symplectic Geometry
2021-08-24 v1 Geometric Topology
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 , fixed at a point, is contractible. We prove this result in the current paper.
Cite
@article{arxiv.2108.09452,
title = {The space of tight contact structures on ${\mathbb R}^3$ is contractible},
author = {Yakov Eliashberg and Nikolai Mishachev},
journal= {arXiv preprint arXiv:2108.09452},
year = {2021}
}
Comments
52 pages, 32 figures