loose_plastik
Loose Legendrians and the plastikstufe
<span class="artikel autor" lang="en"> <a href="#emmy_murphy"> Emmy Murphy </a></span> <span class="artikel autor" lang="de"> Klaus Niederkrüger </span>   <span class="artikel autor"> <a href="#olga_plamenevskaya"> Olga Plamenevskaya </a></span> <span class="artikel autor"> <a href="#andras_stipsicz"> András Stipsicz </a></span>
http://dx.doi.org/10.2140/gt.2013.17.1791
<em>Geom. &amp; Topo.</em>  17 (2013) 1791-1814
2013
gt.jpg
We show that the presence of a plastikstufe induces a certain degree of flexibility in contact manifolds of dimension 2<i>n</i>+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.