Volume 17, issue 3 (2013)

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Loose Legendrians and the plastikstufe

Emmy Murphy, Klaus Niederkrüger, Olga Plamenevskaya and András I Stipsicz

Geometry & Topology 17 (2013) 1791–1814
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 nonisomorphic contact structures become isomorphic after connect-summing with a manifold containing a plastikstufe.

Keywords
contact manifolds, loose Legendrian knots, plastikstufe, overtwisted contact manifolds
Primary: 57R17