On the support genus of Legendrian knots

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ONARAN S.

ARCHIV DER MATHEMATIK, vol.116, no.4, pp.469-479, 2021 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 116 Issue: 4
  • Publication Date: 2021
  • Doi Number: 10.1007/s00013-020-01555-z
  • Journal Name: ARCHIV DER MATHEMATIK
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH, DIALNET
  • Page Numbers: pp.469-479
  • Keywords: Contact structures, Legendrian knots, Open book decompositions, Planar open book decompositions
  • Hacettepe University Affiliated: Yes

Abstract

In this paper, we show that any topological knot or link in S-1 x S-2 sits on a planar page of an open book decomposition whose monodromy is a product of positive Dehn twists. As a consequence, any knot or link type in S-1 x S-2 has a Legendrian representative having support genus zero. We also show this holds for some knots and links in the lens spaces L(p, 1).