Loose Legendrians and the plastikstufe

Abstract

We show that the presence of a plastikstufe induces a certain degree of flexibility in contact manifolds of dimension 2n+1>3. More precisely, we prove that every Legendrian knot whose complement contains a "nice" plastikstufe can be destabilized (and, as a consequence, is loose). As an application, it follows in certain situations that two non-isomorphic contact structures become isomorphic after connect-summing with a manifold containing a plastikstufe.

References in corpus (6)

• Géométrie de contact: de la dimension trois vers les dimensions supérieures
• Loose Legendrian embeddings in high dimensional contact manifolds
• The plastikstufe - a generalization of the overtwisted disk to higher dimensions
• Weak and strong fillability of higher dimensional contact manifolds
• Altering symplectic manifolds by homologous recombination
• Legendrian knots in overtwisted contact structures

Cited by in corpus (8)

• The topology of Stein fillable manifolds in high dimensions I
• The topology of Stein fillable manifolds in high dimensions II
• On plastikstufe, bordered Legendrian open book and overtwisted contact structures
• Non-fillable invariant contact structures on principal circle bundles and left-handed twists
• On positive loops of loose Legendrian embeddings
• An $h$-principle for embeddings transverse to a contact structure
• Exact Lagrangians in four-dimensional symplectisations
• An overtwisted convex hypersurface in higher dimensions