Extended periodic links and HOMFLYPT polynomial

TL;DR

This paper demonstrates that the symmetry properties of extended strongly periodic links are captured by the first coefficients of their HOMFLYPT polynomial, linking topological symmetry with polynomial invariants.

Contribution

It establishes a connection between the symmetry of extended periodic links and specific coefficients of the HOMFLYPT polynomial, providing new insights into link invariants.

Findings

Symmetry of extended periodic links reflected in HOMFLYPT polynomial coefficients

First coefficients of HOMFLYPT polynomial encode link symmetry

Provides a new method to detect link symmetry via polynomial invariants

Abstract

Extended strongly periodic links have been introduced by Przytycki and Sokolov as a symmetric surgery presentation of three-manifolds on which the finite cyclic group acts without fixed points. The purpose of this paper is to prove that the symmetry of these links is reflected by the first coefficients of the HOMFLYPT polynomial.