Loose Legendrians and the plastikstufe

Emmy Murphy, Klaus Niederkrüger, Olga Plamenevskaya, A. Stipsicz

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

We show that the presence of a plastikstufe induces a certain degree of flexibility in contact manifolds of dimension 2n + 1 gt; 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.

Original languageEnglish
Pages (from-to)1791-1814
Number of pages24
JournalGeometry and Topology
Volume17
Issue number3
DOIs
Publication statusPublished - Jul 8 2013

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Legendrian Knot
Contact Manifold
Contact Structure
Complement
Isomorphic
Flexibility

ASJC Scopus subject areas

  • Geometry and Topology

Cite this

Murphy, E., Niederkrüger, K., Plamenevskaya, O., & Stipsicz, A. (2013). Loose Legendrians and the plastikstufe. Geometry and Topology, 17(3), 1791-1814. https://doi.org/10.2140/gt.2013.17.1791

Loose Legendrians and the plastikstufe. / Murphy, Emmy; Niederkrüger, Klaus; Plamenevskaya, Olga; Stipsicz, A.

In: Geometry and Topology, Vol. 17, No. 3, 08.07.2013, p. 1791-1814.

Research output: Contribution to journalArticle

Murphy, E, Niederkrüger, K, Plamenevskaya, O & Stipsicz, A 2013, 'Loose Legendrians and the plastikstufe', Geometry and Topology, vol. 17, no. 3, pp. 1791-1814. https://doi.org/10.2140/gt.2013.17.1791
Murphy E, Niederkrüger K, Plamenevskaya O, Stipsicz A. Loose Legendrians and the plastikstufe. Geometry and Topology. 2013 Jul 8;17(3):1791-1814. https://doi.org/10.2140/gt.2013.17.1791
Murphy, Emmy ; Niederkrüger, Klaus ; Plamenevskaya, Olga ; Stipsicz, A. / Loose Legendrians and the plastikstufe. In: Geometry and Topology. 2013 ; Vol. 17, No. 3. pp. 1791-1814.
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