New proofs of certain finite filling results via Khovanov homology

TL;DR

This paper uses Khovanov homology to prove that hyperbolic twist knots cannot have non-trivial Dehn surgeries resulting in finite fundamental groups, providing a new approach to these topological results.

Contribution

It introduces a novel Khovanov homology-based proof for finite filling results in hyperbolic twist knots, expanding the toolkit for knot theory.

Findings

Hyperbolic twist knots do not admit non-trivial finite surgeries.

Khovanov homology can be used to obstruct certain Dehn surgeries.

New proof technique for finite filling results in knot theory.

Abstract

We give a Khovanov homology proof that hyperbolic twist knots do not admit non-trivial Dehn surgeries with finite fundamental group.