Reeb foliations on S⁵ and contact 5-manifolds violating the Thurston-Bennequin inequality

2009/06/17 by Atsuhide Mori, Mori, Atsuhide · 1 citation
Mathematics · #57R17 #57R20 #57R30 #Advanced Operator Algebra Research #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric Topology (math.GT) #Geometric and Algebraic Topology

paper · pdf · doi:10.48550/arxiv.0906.3237

openalex publication_date 2009/06/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 S⁵, 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.

Citations

• Symplectic manifolds with contact type boundaries

Cited by

• The contact structure on the link of a cusp singularity

Related

• On the violation of Thurston-Bennequin inequality for a certain non-convex hypersurface
• The Reeb foliation arises as a family of Legendrian submanifolds at the end of a deformation of the standard S³ in S⁵
• Morse-Smale characteristic foliations and convexity in contact manifolds
• Contact perturbations of Reebless foliations are universally tight
• Robustly non-convex hypersurfaces in contact manifolds