Seifert surfaces in open books, and a new coding algorithm for links

Rei Furihata; Mikami Hirasawa; Tsuyoshi Kobayashi

doi:10.1112/blms/bdn020

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Seifert surfaces in open books, and a new coding algorithm for links

Rei Furihata·Mikami Hirasawa·Tsuyoshi Kobayashi

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Abstract

We introduce a new standard form of a Seifert surface $F$. In that standard form, $F$ is obtained by successively plumbing flat annuli to a disk $D$, where the gluing regions are all in $D$. We show that any link has a Seifert surface in the standard form, and thereby present a new way of coding a link. We present an algorithm to read the code directly from a braid presentation.

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Rei Furihata, Mikami Hirasawa, Tsuyoshi Kobayashi. 2005-11-07. Seifert surfaces in open books, and a new coding algorithm for links. https://doi.org/10.1112/blms%2Fbdn020

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