Loose Legendrians and the plastikstufe
Emmy Murphy, Klaus Niederkr\"uger, Olga Plamenevskaya, and Andr\'as I., Stipsicz

TL;DR
This paper demonstrates that the presence of a plastikstufe in high-dimensional contact manifolds introduces flexibility, allowing Legendrian knots to be destabilized and making certain contact structures become equivalent after connect-summing.
Contribution
It establishes a link between plastikstufe presence and flexibility in high-dimensional contact topology, showing how it affects Legendrian knots and contact structure isomorphisms.
Findings
Legendrian knots with a 'nice' plastikstufe can be destabilized
Presence of a plastikstufe induces flexibility in contact manifolds
Certain contact structures become isomorphic after connect-summing with a plastikstufe manifold
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.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
