Reeb foliations on S^5 and contact 5-manifolds violating the Thurston-Bennequin inequality

Abstract

This article describes the following results which relate to each other; i) convergence of high dimensional contact structure to codimension one foliation with Reeb component, ii) relation between Nil-type and Sol-type contact submanifolds of S^5, iii) definition of convex Thurston-Bennequin inequality, and iv) generalization of Lutz twist via convex hypersurface theory. The other article concerning non-convex hypersurfaces is included as an appendix.

This is the resubmitted version. 21 pages, 4 figures

References in corpus (3)

• Géométrie de contact: de la dimension trois vers les dimensions supérieures
• The plastikstufe - a generalization of the overtwisted disk to higher dimensions
• On generalizing Lutz twists

Cited by in corpus (9)

• A Hierarchy of Local Symplectic Filling Obstructions for Contact 3-Manifolds
• Algebraic Torsion in higher-dimensional contact manifolds
• On the violation of Thurston-Bennequin inequality for a certain non-convex hypersurface
• Higher dimensional contact topology via holomorphic disks
• Generalizations of twists of contact structures to higher-dimensions via round surgery
• The Reeb foliation arises as a family of Legendrian submanifolds at the end of a deformation of the standard S^3 in S^5
• The contact structure on the link of a cusp singularity
• A note on Mitsumatsu's construction of a leafwise symplectic foliation
• An obstruction for existence of codimension two contact embeddings in a Darboux chart