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