# Complete classification of generalized crossing changes between GOF-knots

## TL;DR

This paper classifies all possible generalized crossing changes between genus one fibered knots by analyzing monodromies with specific arc properties, providing a complete understanding of when such transformations preserve fiberedness.

## Contribution

It offers a complete classification of generalized crossing changes between genus one fibered knots based on monodromy analysis, extending prior partial results.

## Key findings

- Identified all manifolds with genus one fibered knots undergoing generalized crossing changes
- Determined conditions under which such crossing changes preserve fiberedness
- Provided a comprehensive list of all such transformations

## Abstract

We analyze all monodromies of genus one fibered knots that possess clean or once-unclean arcs, and use this to determine all manifolds containing genus one fibered knots with generalized crossing changes resulting in another genus one fibered knot, and classify all such generalized crossing changes between two genus one, fibered knots.