Alternating links have at most polynomially many Seifert surfaces of fixed genus

Joel Hass; Abigail Thompson; Anastasiia Tsvietkova

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arXiv · 1809.10996

Alternating links have at most polynomially many Seifert surfaces of fixed genus

Joel Hass·Abigail Thompson·Anastasiia Tsvietkova

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Abstract

Let $L$ be a non-split prime alternating link with $n>0$ crossings. We show that for each fixed $g$, the number of genus-$g$ Seifert surfaces for $L$ is bounded by an explicitly given polynomial in $n$. The result also holds for all spanning surfaces of fixed Euler characteristic. Previously known bounds were exponential.

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Joel Hass, Abigail Thompson, Anastasiia Tsvietkova. 2018-09-28. Alternating links have at most polynomially many Seifert surfaces of fixed genus. https://arxiv.org/abs/1809.10996

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