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Title: Seifert Surface of the Trefoil
Artist and Designer: Matthew Wright
Materials: Acrylic yarn and wire
Technique: Crochet
Artist’s Statement: If you take a strip of paper, twist
it once and a half, and tape the ends together, the surface you get will
have the trefoil knot as its boundary. But is there an orientable surface—one
with two different sides—that has the trefoil as its boundary? And in general,
what knots or links are the boundary of some orientable surface? It turns
out that they all are: we can always find an orientable surface (in fact,
many) with a given knot or link as its boundary. Such surfaces are called
Seifert surfaces, and they are a useful tool in knot theory.