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

Joel Hass; Abigail Thompson; Anastasiia Tsvietkova

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

Geometric Topology 2024-10-15 v2

Authors: Joel Hass , Abigail Thompson , Anastasiia Tsvietkova

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.

Keywords

alternating links seifert surfaces fixed genus polynomial bound spanning surfaces euler characteristic

Cite

@article{arxiv.1809.10996,
  title  = {Alternating links have at most polynomially many Seifert surfaces of fixed genus},
  author = {Joel Hass and Abigail Thompson and Anastasiia Tsvietkova},
  journal= {arXiv preprint arXiv:1809.10996},
  year   = {2024}
}

Comments

9 pages, 3 figures. To appear in Indiana University Mathematics Journal

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

Abstract

Keywords

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