On generalizing Lutz twists

Abstract

We give a possible generalization of Lutz twist to all dimensions. This reproves the fact that every contact manifold can be given a non-fillable contact structure and also shows great flexibility in the manifolds that can be realized as cores of overtwisted families. We moreover show that $R^{2n+1}$ has at least three distinct contact structures. This version of the paper contains both the texts of the published version of the paper together with an Erratum to the published version appended to the end.

19 pages, 2 figures, and erratum to the published version of the paper

References in corpus (5)

• Géométrie de contact: de la dimension trois vers les dimensions supérieures
• The plastikstufe - a generalization of the overtwisted disk to higher dimensions
• A class of non-fillable contact structures
• On generalizing Lutz twists
• Every contact manifold can be given a non-fillable contact structure

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• On generalizing Lutz twists
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• Almost contact 5-folds are contact
• Reeb foliations on S^5 and contact 5-manifolds violating the Thurston-Bennequin inequality
• Constructions of contact forms on products and piecewise fibered manifolds
• On some examples and constructions of contact manifolds
• On plastikstufe, bordered Legendrian open book and overtwisted contact structures
• Higher dimensional contact topology via holomorphic disks
• Generalizations of twists of contact structures to higher-dimensions via round surgery
• Plastikstufe with toric core
• Near-symplectic 2n-manifolds
• On Legendrian foliations in contact manifold I: Singularities and neighborhood theorems