The almost contact-to-contact existence conjecture
Let be a -dimensional manifold equipped with an almost contact structure, meaning a codimension- cooriented distribution together with a conformally symplectic class on it. Almost contact-to-contact existence conjecture. Any almost contact structure on a manifold 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.
References
Primary source
Francisco Presas, “Geometric decompositions of almost contact manifolds”, arXiv:1211.4696 (2012).
Progress summary
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