Rulings of Legendrian knots as spanning surfaces

Details Rulings of Legendrian knots as spanning surfaces Rulings of Legendrian knots as spanning surfaces

2007-11-22

arxiv.org/abs/0711.3572v1

Mathematics

Geometric Topology

9 pages

Scientific paper

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) knots, we prove 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 (a.k.a. diagram genus) of any knot is an upper bound for the genera of its 2-graded rulings.

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