Loose Legendrians and the plastikstufe

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

Research output: Contribution to journalArticlepeer-review

7 Scopus citations

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.

Original languageEnglish (US)
Pages (from-to)1791-1814
Number of pages24
JournalGeometry and Topology
Volume17
Issue number3
DOIs
StatePublished - Jul 8 2013

ASJC Scopus subject areas

  • Geometry and Topology

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