On the support genus of Legendrian knots

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ONARAN S.

ARCHIV DER MATHEMATIK, cilt.116, sa.4, ss.469-479, 2021 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 116 Sayı: 4
  • Basım Tarihi: 2021
  • Doi Numarası: 10.1007/s00013-020-01555-z
  • Dergi Adı: ARCHIV DER MATHEMATIK
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH, DIALNET
  • Sayfa Sayıları: ss.469-479
  • Anahtar Kelimeler: Contact structures, Legendrian knots, Open book decompositions, Planar open book decompositions
  • Hacettepe Üniversitesi Adresli: Evet

Özet

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).