Approximating C⁰-foliations by contact structures

Bowden, Jonathan (2016): Approximating C⁰-foliations by contact structures. In: Geometric and Functional Analysis, Vol. 26, No. 5: pp. 1255-1296

Abstract

We show that any co-orientable foliation of dimension two on a closed orientable 3-manifold with continuous tangent plane field can be C-0-approximated by both positive and negative contact structures unless all leaves of the foliation are simply connected. As applications we deduce that the existence of a taut C-0-foliation implies the existence of universally tight contact structures in the same homotopy class of plane fields and that a closed 3-manifold that admits a taut C-0-foliation of codimension-1 is not an L-space in the sense of Heegaard-Floer homology.

• Item Type: Journal article
• Faculties: Mathematics, Computer Science and Statistics > Mathematics
• Subjects: 500 Science > 510 Mathematics
• ISSN: 1016-443X
• Language: English