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arXiv · 1211.3895

Loose Legendrians and the plastikstufe

Emmy Murphy·Klaus Niederkrüger·Olga Plamenevskaya·András I. Stipsicz
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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>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.

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Emmy Murphy, Klaus Niederkrüger, Olga Plamenevskaya, András I. Stipsicz. 2012-11-16. Loose Legendrians and the plastikstufe. https://doi.org/10.2140/gt.2013.17.1791

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