Loose Legendrians and the plastikstufe

Murphy, Emmy¹ ; Niederkrüger, Klaus² ; Plamenevskaya, Olga³ ; Stipsicz, András I⁴

¹ Department of Mathematics, MIT, 77 Massachusetts Avenue, Cambridge, MA 02139, USA
² Institut de math., Université Paul Sabatier – Toulouse III, 31062 Toulouse, Cedex 9, France
³ Department of Mathematics, Stony Brook University, Stony Brook, NY 11790, USA
⁴ Rényi Institute of Mathematics, Hungarian Academy of Sciences, 1053 Budapest, Hungary

Geometry & topology, Tome 17 (2013) no. 3, pp. 1791-1814.

Résumé

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.

Détail

DOI : 10.2140/gt.2013.17.1791

Classification : 57R17
Keywords: contact manifolds, loose Legendrian knots, plastikstufe, overtwisted contact manifolds

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