Existence and classification of overtwisted contact structures in all dimensions
By M. S. Borman, Y. Eliashberg, Emmy Murphy. 2014
186 citations recorded by the source corpus.
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.
Subfields: Computational Theory and Mathematics, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/d952471e052bbd343dcc275473bf49044a0b8668
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In Computational Theory and Mathematics
In Geometry and Topology
In Mathematical Physics
Citations in the corpus
- Symplectic homology and the Eilenberg-Steenrod axioms (2015, unknown): “This is proved in the same way as non-fillability of overtwisted contact manifolds [10, 21], using filling by holomorphic discs in the symplectic manifold (0, 1) × ∂−W ∪ W .”
- Contact homology and virtual fundamental cycles (2015, background): “Overtwisted contact structures are classified completely by an h-principle due to Eliashberg [Eli89] in dimension three and Borman–Eliashberg– Murphy [BEM15] in general.”