Approximating C⁰-foliations by contact structures

Bowden, Jonathan (2016): Approximating C⁰-foliations by contact structures. In: Geometric and Functional Analysis, Bd. 26, Nr. 5: S. 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.

• Dokumententyp: Zeitschriftenartikel
• Fakultät: Mathematik, Informatik und Statistik > Mathematik
• Themengebiete: 500 Naturwissenschaften und Mathematik > 510 Mathematik
• ISSN: 1016-443X
• Sprache: Englisch