Genus and fibredness of certain three-bridge links

TL;DR

This paper constructs taut Seifert surfaces for specific three-bridge links, determines their fibredness, and extends results to satellite knots with patterns from two-bridge links, advancing understanding of link genus and fibredness.

Contribution

It introduces a method to determine genus and fibredness for certain three-bridge links and related satellite knots, filling gaps in previous classifications.

Findings

Constructed taut Seifert surfaces for specific three-bridge links

Established fibredness criteria for these links

Determined genus and fibredness of related satellite knots

Abstract

For each three-bridge link of a certain form, we construct a taut Seifert surface for the link and establish whether the link is fibred. Using this, we also give the genus and fibredness of satellite knots whose pattern is constructed from a two-component two-bridge link in the case not addressed by work of Hirasawa and Murasugi.