Existence and classification of overtwisted contact structures in all dimensions

Matthew Strom Borman Department of Mathematics, Stanford University Yakov Eliashberg Department of Mathematics, Stanford University Emmy Murphy Department of Mathematics, Massachusetts Institute of Technology

Geometric Analysis and Geometric Topology mathscidoc:1701.15002

Acta Mathematica, 215, (2), 281-361, 2014.10
We establish a parametric extension$h$-principle for overtwisted contact structures on manifolds of all dimensions, which is the direct generalization of the 3-dimensional result from [12]. It implies, in particular, that any closed manifold admits a contact structure in any given homotopy class of almost contact structures.
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@inproceedings{matthew2014existence,
  title={Existence and classification of overtwisted contact structures in all dimensions},
  author={Matthew Strom Borman, Yakov Eliashberg, and Emmy Murphy},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203405921548810},
  booktitle={Acta Mathematica},
  volume={215},
  number={2},
  pages={281-361},
  year={2014},
}
Matthew Strom Borman, Yakov Eliashberg, and Emmy Murphy. Existence and classification of overtwisted contact structures in all dimensions. 2014. Vol. 215. In Acta Mathematica. pp.281-361. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203405921548810.
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