# A Note on the Orderability of Dehn Fillings of the Manifold $v2503$

## TL;DR

This paper demonstrates that all Dehn fillings of the manifold v2503 with slopes in (-∞, -1) produce non-orderable spaces, supporting the L-space conjecture.

## Contribution

It provides the first comprehensive analysis of the orderability of Dehn fillings for manifold v2503 across a range of slopes.

## Key findings

- Dehn fillings with slopes in (-∞, -1) are non-orderable.
- Supports the L-space conjecture for manifold v2503.
- All relevant fillings in the specified interval are non-orderable.

## Abstract

We show that Dehn filling on the manifold $v2503$ results in a non-orderable space for all rational slopes in the interval $(-\infty , -1)$. This is consistent with the L-space conjecture, which predicts that all fillings will result in a non-orderable space for this manifold.