$C^0$ Approximations of foliations
By W. Kazez, R. Roberts. 2015
48 citations recorded by the source corpus.
Suppose that $\mathcal F$ is a transversely oriented, codimension one foliation of a connected, closed, oriented 3-manifold. Suppose also that $\mathcal F$ has continuous tangent plane field and is {\sl taut}; that is, closed smooth transversals to $\mathcal F$ pass through every point of $M$. We show that if $\mathcal F$ is not the product foliation $S^1\times S^2$, then $\mathcal F$ can be $C^0$ approximated by weakly symplectically fillable, universally tight, contact structures. This extends work of Eliashberg-Thurston on approximations of taut, transversely oriented $C^2$ foliations to the class of foliations that often arise in branched surface constructions of foliations. This allows applications of contact topology and Floer theory beyond the category of $C^2$ foliated spaces.
Subfields: Applied Mathematics, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/26d0ad22beb3042a9a9c9e9cf011d2c38bd6ecc0
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In Applied Mathematics
In Geometry and Topology
In Mathematical Physics
Citations in the corpus
- Approximating C0-foliations by contact structures (2015, methodology): “ taut foliations has been obtained in [17] using rather different methods. Moreover, Kazez and Roberts have refined their methods to give an independent proof of Theorem 1.2 for general taut foliations [18] without any assumptions other than that the manifold is not S2 × S1 with the product foliation.”