Rulings of Legendrian knots as spanning surfaces

Tamás Kálmán

Vol. 237 (2008), No. 2, 287–297

DOI: 10.2140/pjm.2008.237.287

Abstract

Each ruling of a Legendrian link can be naturally treated as a surface. For knots, the ruling is 2-graded if and only if the surface is orientable. For 2-graded rulings of homogeneous (in particular, alternating and positive) knots, we show that the genus of this surface is at most the genus of the knot. While this is not true in general, we do prove that the canonical genus of any knot is an upper bound for the genera of its 2-graded rulings.

Keywords

knot, Legendrian knot, genus, canonical genus, ruling, spanning surface

Mathematical Subject Classification 2000

Primary: 53D12, 57M25

Milestones

Received: 6 December 2007

Revised: 14 March 2008

Accepted: 19 May 2008

Published: 1 October 2008