[2206.11200] Refinement of the unorientable $4$ genus of torus knots

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

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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.