Minimal genus Seifert surface for 11 crossing alternating knots

Neetal Neel

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arXiv · 2312.00208

Minimal genus Seifert surface for 11 crossing alternating knots

Neetal Neel

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Abstract

Kakimizu complexes have been found for several classes of links. O.Kakimizu found the Kakimizu complexes of knots with crossing number less than or equal to 10. Hatcher and Thurston found the 0-skeleton of the Kakimizu complex of 2-bridge links. Sakuma later generalized the result for special arborescent links and found the Kakimizu complexes for the same. Jessica Banks gave a complete proof of results announced by Hirasawa and Sakuma, describing explicitly the Kakimizu complexes of non-split, prime special alternating links. The Kakimizu complexes of prime, non-split alternating links have finite number of vertices. In this paper we compute the Kakimizu complexes for all $11$ crossing prime, alternating knots, explicitly describing each of them. For most knots and links we use known algorithms. The rest of the Kakimizu complexes were found by using Murasugi sums and sutured manifold theory developed by Gabai, Scharlemann, Kakimizu and others.

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Neetal Neel. 2023-11-30. Minimal genus Seifert surface for 11 crossing alternating knots. https://arxiv.org/abs/2312.00208

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