Sutured Manifold Decomposition of 7_7

While packing for my move and sorting through old papers, I’ve come across several drawings from my ill spent youth (aka grad school).

Here we’ve done Gabai’s sutured manifold decomposition on the exterior of a Seifert surface for the knot 7_7 in Rolfsen’s table, thereby showing it is a minimal genus Seifert surface. The Seifert surface used is the one obtained from Seifert’s algorithm on the knot diagram shown. Note (1) our viewpoint is from the inside of the sutured manifold and (2) our first decomposition disconnects the sutured manifold to give the two sutured manifolds beginning the bottom two lines.

7_7-Sutured Manifold Decomp

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~ by Ken Baker on July 9, 2008.

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