Periodic spanning surfaces of periodic knots

Stanislav Jabuka

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arXiv · 2101.04668

Periodic spanning surfaces of periodic knots

Stanislav Jabuka

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Abstract

Edmonds famously proved that every periodic knot of genus g possesses an equivariant Seifert surface of genus g. We show that this is not true if one instead considers nonorientable spanning surfaces of a periodic knot. We demonstrate by example that the difference between the first Betti number of an equivariant and a nonequivariant nonorientable spanning surface of a periodic knot, can be arbitrarily large.

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Stanislav Jabuka. 2021-01-12. Periodic spanning surfaces of periodic knots. https://arxiv.org/abs/2101.04668

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