Rulings of Legendrian knots as spanning surfaces
Geometric Topology
2007-11-26 v1 Symplectic Geometry
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) 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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Cite
@article{arxiv.0711.3572,
title = {Rulings of Legendrian knots as spanning surfaces},
author = {Tamás Kálmán},
journal= {arXiv preprint arXiv:0711.3572},
year = {2007}
}
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9 pages