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Download a PDF of the paper entitled On a Refinement of the Non-Orientable $4$-genus of Torus Knots by Joshua M. Sabloff

overview: In formulating an undirected analogue of the Milner conjecture for the $4$ genus of torus knots, Batson proposes a smooth and undirected analog in $B^4$ for a torus knot given in $S^. We have developed an elegant structure that produces a possible span surface.$3. Lobb showed that the Batson surface does not always minimize the unorientable $4$ genus, but proves that it always minimizes among surfaces sharing a common Euler number. . Also, the bound on the class of torus knots for which the Batson surface is an unorientable $4$ genus minimization, completely completes the possible pairs of normal Euler numbers and first Betty numbers for unorientable surfaces. Decide.

Submission history

From: Joshua M. Sabloff [view email]

[v1]

Wed, Jun 22, 2022 16:33:59 UTC (22 KB)
[v2]

Wednesday, March 15, 2023 13:24:33 UTC (23 KB)

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