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ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Loose Legendrians and the plastikstufe

Emmy Murphy, Klaus Niederkrüger, Olga Plamenevskaya and András I Stipsicz

Geometry & Topology 17 (2013) 1791–1814
Abstract

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.

Keywords
contact manifolds, loose Legendrian knots, plastikstufe, overtwisted contact manifolds
Mathematical Subject Classification 2010
Primary: 57R17
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
Authors
Emmy Murphy
Department of Mathematics
MIT
77 Massachusetts Avenue
Cambridge, MA 02139
USA
Klaus Niederkrüger
Institut de math.
Université Paul Sabatier – Toulouse III
31062 Toulouse, Cedex 9
France
http://www.math.univ-toulouse.fr/~niederkr/
Olga Plamenevskaya
Department of Mathematics
Stony Brook University
Stony Brook, NY 11790
USA
András I Stipsicz
Rényi Institute of Mathematics
Hungarian Academy of Sciences
1053 Budapest
Hungary
http://www.renyi.hu/~stipsicz