Loose Legendrians and the plastikstufe
Author(s)Murphy, Emmy; Niederkrüger, Klaus; Plamenevskaya, Olga; Stipsicz, András I
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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 nonisomorphic contact structures become isomorphic after connect-summing with a manifold containing a plastikstufe.
DepartmentMassachusetts Institute of Technology. Department of Mathematics
Geometry and Topology
Mathematical Sciences Publishers
Murphy, Emmy, Klaus Niederkrüger, Olga Plamenevskaya, and András I Stipsicz. “Loose Legendrians and the Plastikstufe.” Geometry & Topology 17, no. 3 (2013): 1791–1814.