English

Loose Legendrians and the plastikstufe

Symplectic Geometry 2014-11-11 v1 Geometric Topology

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.

Keywords

Cite

@article{arxiv.1211.3895,
  title  = {Loose Legendrians and the plastikstufe},
  author = {Emmy Murphy and Klaus Niederkrüger and Olga Plamenevskaya and András I. Stipsicz},
  journal= {arXiv preprint arXiv:1211.3895},
  year   = {2014}
}