I don’t mean to give off the impression that I only think about Seifert surfaces, but they’re fun to draw…

This one, a torus minus two disks, is bounded by the Whitehead link L. The faces of the unit ball of H_{2}(S^{3}\L, boundary;R) with respect to the Thurston norm are all fibered, so in particular this surface is the fiber of a bundle S^{3}\L ➝ S^{1}; take my word for it that its homology class lies in the cone on the interior of the faces.

The theory also shows that this is a norm-minimizing surface for L, so the genus of L is 1.

I’m slowly writing some notes on the Thurston norm with the goal of having something reasonable by September.