A class of non-fillable contact structures

Abstract

A geometric obstruction, the so called "plastikstufe", for a contact structure to not being fillable has been found by K. Niederkruger. This generalizes somehow the concept of overtwisted structure to dimensions higher than 3. This paper elaborates on the theory showing a big number of closed contact manifolds with a "plastikstufe". They are the first examples of non-fillable contact closed high-dimensional manifolds. In particular we show that $S^3\times {\prod }_j{\Sigma }_j$, for $g({\Sigma }_j)\ge 2$, possesses this kind of contact structure and so any connected sum with those manifolds also does it.

19 pages, 4 figures

References in corpus (3)

• Géométrie de contact: de la dimension trois vers les dimensions supérieures
• Lectures on open book decompositions and contact structures
• The plastikstufe - a generalization of the overtwisted disk to higher dimensions

Cited by in corpus (11)

• The plastikstufe - a generalization of the overtwisted disk to higher dimensions
• Weak and strong fillability of higher dimensional contact manifolds
• On generalizing Lutz twists
• Every contact manifold can be given a non-fillable contact structure
• Some remarks on the size of tubular neighborhoods in contact topology and fillability
• On some examples and constructions of contact manifolds
• On plastikstufe, bordered Legendrian open book and overtwisted contact structures
• On properties of Bourgeois contact structures
• Higher dimensional contact topology via holomorphic disks
• On positive loops of loose Legendrian embeddings
• 5-dimensional Bourgeois contact structures are tight