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Loose Legendrians and the
plastikstufe
Emmy Murphy, Klaus Niederkrüger, Olga Plamenevskaya and András I Stipsicz |
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Geometry & Topology 17 (2013) 1791–1814
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Abstract |
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We show that the presence of a plastikstufe induces a certain degree of flexibility in contact manifolds of dimension . 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. |
Keywords
contact manifolds, loose Legendrian knots, plastikstufe,
overtwisted contact manifolds
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Mathematical Subject Classification 2010
Primary: 57R17
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References |
Publication
Received: 18 December 2012
Revised: 3 March 2013
Accepted: 8 April 2013
Published: 8 July 2013
Proposed: Yasha Eliashberg
Seconded: Leonid Polterovich, Jean-Pierre Otal
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Authors |
| Emmy Murphy | |
| Department of Mathematics MIT 77 Massachusetts Avenue Cambridge, MA 02139 USA |
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| Klaus Niederkrüger | |
| Institut de math. Université Paul Sabatier – Toulouse III 31062 Toulouse, Cedex 9 France |
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| http://www.math.univ-toulouse.fr/~niederkr/ | |
| Olga Plamenevskaya | |
| Department of Mathematics Stony Brook University Stony Brook, NY 11790 USA |
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| András I Stipsicz | |
| Rényi Institute of Mathematics Hungarian Academy of Sciences 1053 Budapest Hungary |
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| http://www.renyi.hu/~stipsicz | |
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