Loose Legendrians and the plastikstufe

Murphy, E. and Niederkrüger, K. and Plamenevskaya, O. and Stipsicz, András (2013) Loose Legendrians and the plastikstufe. Geometry and Topology, 17 (3). pp. 1791-1814. ISSN 1465-3060

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Abstract

We show that the presence of a plastikstufe induces a certain degree of flexibility in contact manifolds of dimension 2n + 1 gt; 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.

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