Baader, Sebastian; Cieliebak, Kai; Vogel, Thomas Legendrian ribbons in overtwisted contact structures. (English) Zbl 1229.57003 J. Knot Theory Ramifications 18, No. 4, 523-529 (2009). Summary: We show that a null-homologous transverse knot \(K\) in the complement of an overtwisted disk in a contact 3-manifold is the boundary of a Legendrian ribbon if and only if it possesses a Seifert surface \(S\) such that the self-linking number of \(K\) with respect to \(S\) satisfies \(\text{sl}(K,S)=-\chi(S)\). In particular, every null-homologous topological knot type in an overtwisted contact manifold can be represented by the boundary of a Legendrian ribbon. Finally, we show that a contact structure is tight if and only if every Legendrian ribbon minimizes genus in its relative homology class. Cited in 2 Documents MSC: 57M25 Knots and links in the \(3\)-sphere (MSC2010) 57R17 Symplectic and contact topology in high or arbitrary dimension 53D10 Contact manifolds (general theory) Keywords:Legendrian ribbon; transverse knot; overtwisted disk; contact structure PDFBibTeX XMLCite \textit{S. Baader} et al., J. Knot Theory Ramifications 18, No. 4, 523--529 (2009; Zbl 1229.57003) Full Text: DOI arXiv References: [1] Baader S., Osaka J. Math. 42 pp 257– [2] Bennequin D., Astérisque pp 83– [3] DOI: 10.5802/aif.1288 · Zbl 0756.53017 · doi:10.5802/aif.1288 [4] DOI: 10.1016/B978-044451452-3/50004-6 · doi:10.1016/B978-044451452-3/50004-6 [5] DOI: 10.1016/S0001-8708(02)00027-0 · Zbl 1047.57006 · doi:10.1016/S0001-8708(02)00027-0 [6] DOI: 10.1016/S0040-9383(96)00035-3 · Zbl 0904.57006 · doi:10.1016/S0040-9383(96)00035-3 [7] DOI: 10.1007/s002220050245 · Zbl 0902.57007 · doi:10.1007/s002220050245 [8] DOI: 10.1016/0040-9383(92)90017-C · Zbl 0763.57008 · doi:10.1016/0040-9383(92)90017-C This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.