# A counterexample to Batson's conjecture

## TL;DR

This paper presents a counterexample to Batson's conjecture by demonstrating that the torus knot T_{4,9} bounds a smooth M"obius band in the 4-ball, challenging previous assumptions about non-orientable slice genera.

## Contribution

The authors provide the first known counterexample to Batson's non-orientable Milnor conjecture using explicit construction.

## Key findings

- T_{4,9} bounds a smooth M"obius band in the 4-ball
- Counterexample disproves Batson's conjecture on non-orientable slice genus
- Advances understanding of non-orientable surfaces in 4-dimensional topology

## Abstract

We show that the torus knot $T_{4,9}$ bounds a smooth M\"obius band in the $4$-ball, giving a counterexample to Batson's non-orientable analogue of Milnor's conjecture on the smooth slice genera of torus knots.