Seifert surfaces – Saul Schleimer and Henry Segerman

“We are geometric topologists, and we are interested in visualising knots, surfaces and three-manifolds. Prompted by this, we design 3D printed models of these objects. This movie shows and explains some of the relevant mathematics.

Seifert surfaces are spanning surfaces for knots, in a similar way to how soap films span wire loops. The Seifert surfaces for torus knots have a beautiful representation as the Milnor fibers of polynomial singularities.”

"The mathematician's patterns, like the painter's or the poet's, must be beautiful; the ideas, like the colours or the words, must fit together in a harmonious way. "
G H Hardy, A Mathematician's Apology (London 1941).
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