Loose Legendrians and the plastikstufe

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...

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Bibliographic Details
Main Authors: Murphy, Emmy (Contributor), Niederkrüger, Klaus (Author), Plamenevskaya, Olga (Author), Stipsicz, András I (Author)
Other Authors: Massachusetts Institute of Technology. Department of Mathematics (Contributor)
Format: Article
Language:English
Published: Mathematical Sciences Publishers, 2015-01-22T15:28:14Z.
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Online Access:Get fulltext
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042 |a dc 
100 1 0 |a Murphy, Emmy  |e author 
100 1 0 |a Massachusetts Institute of Technology. Department of Mathematics  |e contributor 
100 1 0 |a Murphy, Emmy  |e contributor 
700 1 0 |a Niederkrüger, Klaus  |e author 
700 1 0 |a Plamenevskaya, Olga  |e author 
700 1 0 |a Stipsicz, András I  |e author 
245 0 0 |a Loose Legendrians and the plastikstufe 
260 |b Mathematical Sciences Publishers,   |c 2015-01-22T15:28:14Z. 
856 |z Get fulltext  |u http://hdl.handle.net/1721.1/93118 
520 |a 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. 
520 |a National Science Foundation (U.S.) (Grant DMS-0943787) 
520 |a European Science Foundation 
546 |a en_US 
655 7 |a Article 
773 |t Geometry and Topology 

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