Cyclic branched covers of alternating knots

TL;DR

This paper proves that for any integer n > 2, the n-fold cyclic branched cover uniquely determines an alternating prime knot in the 3-sphere, establishing a strong knot identification property.

Contribution

It establishes that the n-fold cyclic branched cover uniquely determines an alternating prime knot for all n > 2, extending previous results in knot theory.

Findings

n-fold cyclic branched cover uniquely determines the knot

The result holds for all integers n > 2

Provides a new tool for knot identification

Abstract

For any integer n > 2, the n-fold cyclic branched cover M of an alternating prime knot K in the 3-sphere determines K, meaning that if K is a knot in the 3-sphere that is not equivalent to K then its n-fold cyclic branched cover cannot be homeomorphic to M.