A classification of transitive links and periodic links

TL;DR

This paper extends the concept of periodic links to transitive links in 3-manifolds, providing a complete classification in the 3-sphere and analyzing their polynomial invariants from various perspectives.

Contribution

It introduces transitive links in 3-manifolds and offers a comprehensive classification theorem for these links in the 3-sphere, along with polynomial invariant analysis.

Findings

Complete classification of transitive links in ^3

Relation between link polynomials of transitive links and factor links

Analysis of polynomial invariants from multiple aspects

Abstract

We generalized the periodic links to \emph{transitive} links in a $3$-manifold $M$. We find a complete classification theorem of transitive links in a $3$-dimensional sphere $\mathbb{R}^3$. We study these links from several different aspects including polynomial invariants using the relation between link polynomials of a transitive link and its factor links.