What is a Seifert surface? Very loosly, a Serifert surace is a two sided surface whos boundary is a knot. You may think of this surface as the result of taking a wire frame of a knot and dipping it into some soapy water and taking it out. The result will be a surface like this.
This particular surface is a surface for the trefoil knot obtained by the construction stated in Seifert's algorithm, outlined in my notes. Also fun picture of trefoil knot to the right! or below!
And why did I make this? you ask? well.. I kind of looks sick, plus the mathematics it enables is of a certain quality I wont get into here.
Stuff to download: Seifert surface for Trefoil knot