Geometry & Topology

Transversal torus knots

John B Etnyre

Full-text: Open access


We classify positive transversal torus knots in tight contact structures up to transversal isotopy.

Article information

Geom. Topol., Volume 3, Number 1 (1999), 253-268.

Received: 16 June 1999
Accepted: 27 August 1999
First available in Project Euclid: 21 December 2017

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 57M50: Geometric structures on low-dimensional manifolds 57M25: Knots and links in $S^3$ {For higher dimensions, see 57Q45}
Secondary: 53C15: General geometric structures on manifolds (almost complex, almost product structures, etc.)

tight contact structure transversal knots torus knots


Etnyre, John B. Transversal torus knots. Geom. Topol. 3 (1999), no. 1, 253--268. doi:10.2140/gt.1999.3.253.

Export citation


  • B Aebisher, et al, Symplectic Geometry, Progress in Math. 124, Birkhäuser, Basel, Boston and Berlin (1994)
  • S Akbulut, R Matveev, A note on contact structures, Pacific J. Math. 182 (1998) 201-204
  • D Bennequin, Entrelacements et équations de Pfaff, Asterisque, 107–108 (1983) 87–161
  • Y Chekanov, Differential algebras of Legendrian links, Preprint (1997)
  • Y Eliashberg, Contact 3–manifolds twenty years since J Martinet's work, Ann. Inst. Fourier, 42 (1992) 165–192
  • Y Eliashberg, Legendrian and transversal knots in tight contact 3–manifolds, Topological Methods in Modern Mathematics (1993) 171–193
  • Y Eliashberg, M Fraser, Classification of topologically trivial Legendrian knots, from: “Geometry, topology, and dynamics” (Montreal, PQ, 1995), CRM Proc. Lecture Notes, 15, Amer. Math. Soc. Providence, RI (1998) 17–51,
  • J Etnyre, Symplectic Constructions on $4$–Manifolds, Dissertation, University of Texas (1996)
  • D Fuchs, S Tabachnikov, Invariants of Legendrian and transverse knots in the standard contact space, Topology, 36 (1997) 1025–1053
  • E Giroux, Convexité en topologie de contact, Comment. Math. Helvetici, 66 (1991) 637–677
  • E Giroux, Topologie de contact en dimension $3$ (autour des travaux de Yakov Eliashberg), Séminaire Bourbaki, Vol. 1992/93. Astérisque, 216, Exp. No. 760, 3 (1993) 7–33
  • Y Kanda, The classification of tight contact structures on the 3–torus, Comm. in Anal. and Geom. 5 (1997) 413–438
  • R Kirby, Problems in low-dimensional topology, AMS/IP Stud. Adv. Math. 2.2, Amer. Math. Soc. and International Press (1997)
  • S Makar–Limanov, Tight contact structures on solid tori, Trans. Amer. Math. Soc. 350 (1998) 1013–104
  • L Rudolph, An obstruction to sliceness via contact geometry and “classical” gauge theory, Invent. Math. 119 (1995) 155–163