On the fibration of augmented link complements

TL;DR

This paper characterizes when augmented link complements are fibered by associating a spanning surface and a graph, showing fibration corresponds to the graph being a tree, and explores how fibration is preserved under Dehn filling.

Contribution

It provides a graph-theoretic criterion for the fibration of augmented link complements and demonstrates that all locally alternating augmented links are fibered.

Findings

Fibration corresponds to the associated graph being a tree.

Fibration is preserved under certain Dehn fillings.

All locally alternating augmented links are fibered.

Abstract

We study the fibration of augmented link complements. Given the diagram of an augmented link we associate a spanning surface and a graph. We then show that this surface is a fiber for the link complement if and only if the associated graph is a tree. We further show that fibration is preserved under Dehn filling on certain components of these links. This last result is then used to prove that within a very large class of links, called locally alternating augmented links, every link is fibered.