The almost contact-to-contact existence conjecture

Let MM be a (2n+1)(2n+1)-dimensional manifold equipped with an almost contact structure, meaning a codimension-11 cooriented distribution together with a conformally symplectic class on it. Almost contact-to-contact existence conjecture. Any almost contact structure on a manifold MM admits a deformation in its homotopy class of almost contact structures to a contact structure. This is the fundamental existence conjecture of contact topology: it asserts that the formal almost contact condition is sufficient for the existence of a contact structure in the same homotopy class. The supplied text does not indicate whether the conjecture has been resolved.

Sources & referencesView supporting material

Primary source

Francisco Presas, “Geometric decompositions of almost contact manifolds”, arXiv:1211.4696 (2012).

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