Band surgeries and crossing changes between fibered links

TL;DR

This paper characterizes how specific surface modifications like band surgeries and crossing changes affect fibered links and their monodromy, introducing new operations and providing a comprehensive understanding of these transformations.

Contribution

It introduces a characterization of band surgeries and crossing changes on fibered links, along with a new operation called Generalized Hopf banding, advancing the understanding of fibered link modifications.

Findings

Characterization of cutting arcs that produce new fiber surfaces

Introduction of Generalized Hopf banding operation

Analysis of monodromy changes due to surface modifications

Abstract

We characterize cutting arcs on fiber surfaces that produce new fiber surfaces, and the changes in monodromy resulting from such cuts. As a corollary, we characterize band surgeries between fibered links and introduce an operation called Generalized Hopf banding. We further characterize generalized crossing changes between fibered links, and the resulting changes in monodromy.