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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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