Quotients of Definite Periodic Knots are Definite

TL;DR

This paper proves that the quotient of a definite periodic knot remains definite by analyzing equivariant minimal genus Seifert surfaces, contributing to the understanding of knot properties under periodic symmetries.

Contribution

It introduces a new method using equivariant minimal genus Seifert surfaces to establish the preservation of definiteness under knot quotients.

Findings

Quotients of definite periodic knots are definite.

The proof relies on properties of equivariant minimal genus Seifert surfaces.

Advances understanding of knot invariants under symmetry operations.

Abstract

A knot $K$ is definite if $|\sigma(K)| = 2g(K)$. We prove that the quotient of a definite periodic knot is definite by considering equivariant minimal genus Seifert surfaces.