Fibered knots and links in lens spaces

TL;DR

This paper explores fibered knots and links in lens spaces, providing explicit link diagrams and analyzing their compatibility with contact structures, especially in the case of $L(p,1)$ with $p eq 0$.

Contribution

It introduces a method to obtain mixed link diagrams for fibered links in lens spaces and examines their compatibility with contact structures, including explicit lift diagrams in $S^3$.

Findings

Constructed mixed link diagrams for fibered links in lens spaces.

Showed compatibility of certain links with standard contact structures in $L(p,1)$.

Provided explicit lift diagrams in $S^3$ for analysis.

Abstract

We take advantage of the correspondence between fibered links, open book decompositions and contact structures on a closed connected 3-dimensional manifold to determine a mixed link diagram presentation for a particular fibered link $L$ in the lens space $L(p,q)$. Moreover, we construct a diagram for the lift of $L$ in the 3-sphere $S^3$ in order to show that, for $q=1$, $L$ is compatible with the standard contact structure of $L(p,1)$ when $p \leq -1$.