Seifert surface for (3,3) torus link

prusaprinters

<p>This is joint work with Saul Schleimer.</p><p>A torus link is a link that can be drawn on a torus. A Seifert surface spans its link, somewhat like a soap-film clinging to its supporting wire-frame. The surface acts as a bridge between the 1-dimensional link and the 3-dimensional space it lives in.</p><p>The torus links and their Seifert surfaces live most naturally in the 3-sphere, a higher dimensional version of the more familiar sphere. We transfer our sculptures to Euclidean 3-space using stereographic projection. The Seifert surface is cut out of the 3-sphere by the Milnor fibers of the corresponding algebraic singularity. We parametrize the Milnor fiber, following the work of Tsanov, via fractional automorphic forms. These give a map from SL(2,R), the canonical geometry of the torus link complement, to the 3-sphere.</p><p>The patterns on each Seifert surface arise from two applications of the Schwarz-Christoffel theory of complex analysis, turning a Euclidean triangle into a hyperbolic one. We used our <a href="https://www.printables.com/model/167512-schleimer-segerman-makers-mark">maker's mark</a> for the pattern.</p><p>Category: Math Art</p>