# The disk complex and 2-bridge knots

## TL;DR

This paper provides an alternative proof that all genus one 1-bridge positions of non-trivial 2-bridge knots are stabilizations, clarifying their structure within knot theory.

## Contribution

It offers a new proof of a known result regarding the stabilization of genus one 1-bridge positions in 2-bridge knots.

## Key findings

- All genus one 1-bridge positions of non-trivial 2-bridge knots are stabilizations
- Provides an alternative proof to a known theorem in knot theory
- Enhances understanding of the disk complex in relation to 2-bridge knots

## Abstract

We give an alternative proof of a result of Kobayashi and Saeki that every genus one $1$-bridge position of a non-trivial $2$-bridge knot is a stabilization.