The realizability conjecture for unknown points of T(2,n)T(2,n)

For an odd integer nn, let T(2,n)T(2,n) denote the corresponding torus knot, and let (e,h)(e,h) denote the pair consisting of the normal Euler number and nonorientable genus of a surface bounded by the knot. The pairs whose realizability is not determined by the preceding results are called unknown points. The realizability conjecture for T(2,n)T(2,n). For T(2,n)T(2,n) with nn odd, all unknown points are not realizable. This would complete the realizability classification for these torus knots, since the remaining pairs are already known to be realizable or not realizable.

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Primary source

Samantha Allen, “Nonorientable surfaces bounded by knots: a geography problem”, arXiv:2007.14332 (2020).

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