The number of surfaces of fixed genus in an alternating link complement

Joel Hass; Abigail Thompson; Anastasiia Tsvietkova

doi:10.1093/imrn/rnw075

The number of surfaces of fixed genus in an alternating link complement

Geometric Topology 2019-04-12 v2

Authors: Joel Hass , Abigail Thompson , Anastasiia Tsvietkova

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Abstract

Let $L$ be a prime alternating link with $n$ crossings. We show that for each fixed $g$ , the number of genus $g$ incompressible surfaces in the complement of $L$ is bounded by a polynomial in $n$ . Previous bounds were exponential in $n$ .

Keywords

alternating link link complement incompressible surfaces fixed genus polynomial bound prime alternating link crossings

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@article{arxiv.1508.03680,
  title  = {The number of surfaces of fixed genus in an alternating link complement},
  author = {Joel Hass and Abigail Thompson and Anastasiia Tsvietkova},
  journal= {arXiv preprint arXiv:1508.03680},
  year   = {2019}
}

Comments

9 pages, 2 figures, to appear in International Mathematics Research Notices

The number of surfaces of fixed genus in an alternating link complement

Abstract

Keywords

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