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Each ruling of a Legendrian link can be naturally treated as a surface. Forknots, the ruling is 2-graded if and only if the surface is orientable. For2-graded rulings of homogeneous (in particular, alternating) knots, we provethat the genus of this surface is at most the genus of the knot. While this isnot true in general, we do prove that the canonical genus (a.k.a. diagramgenus) of any knot is an upper bound for the genera of its 2-graded rulings.

Rulings of Legendrian knots as spanning surfaces