A remark on the counterexample to the unknotting number conjecture

TL;DR

This paper verifies a surprising counterexample to the unknotting number conjecture involving a specific knot and its mirror, challenging previous assumptions in knot theory.

Contribution

It provides a direct verification of a counterexample to the unknotting number conjecture discovered using computational tools.

Findings

Confirmed that u(7_1#_1)  5, less than u(7_1)+u(_1)

Validated the counterexample through direct computation

Challenges existing beliefs about unknotting numbers in knot theory

Abstract

By using Snappy, M. Brittenham and S. Hermiller discovered a very surprising example that $u(7_1\#\overline{7_1})\leq 5<6=u(7_1)+u(\overline{7_1})$, where $7_1$ is the $(2,7)$-torus knot and $\overline{7_1}$ is its mirror image. Based on their work, we give a direct verification of this fact.