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Existence and classification of overtwisted contact structures in all dimensions

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Acta Mathematica

Abstract

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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Author information

Authors and Affiliations

  1. Department of Mathematics, Stanford University, 450 Serra Mall, Stanford, CA, 94305-2125, U.S.A.

    Matthew Strom Borman & Yakov Eliashberg

  2. Department of Mathematics, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA, 02139-4307, U.S.A.

    Emmy Murphy

Authors
  1. Matthew Strom Borman
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  2. Yakov Eliashberg
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  3. Emmy Murphy
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Corresponding author

Correspondence to Yakov Eliashberg.

Additional information

To Misha Gromov with admiration.

M. S. B. was partially supported by NSF grant DMS-1304252, Y. E. was partially supported by NSF grant DMS-1205349, E. M. was partially supported by NSF grant DMS-1510305.

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Borman, M.S., Eliashberg, Y. & Murphy, E. Existence and classification of overtwisted contact structures in all dimensions. Acta Math 215, 281–361 (2015). https://doi.org/10.1007/s11511-016-0134-4

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  • DOI: https://doi.org/10.1007/s11511-016-0134-4

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