Invariants of weakly successively almost positive links

TL;DR

This paper introduces and studies new classes of links called successively almost positive and weakly successively almost positive, analyzing their polynomial invariants, signatures, minimal genus, and fibering properties, extending known results in link theory.

Contribution

It defines the classes of successively almost positive links and extends key properties and theorems to these classes, including polynomial invariants and fibering criteria.

Findings

Extended properties of polynomial invariants and signatures for these links

Proved minimal genus and fibering properties for the new classes

Established a fibering extension of Scharlemann-Thompson's theorem

Abstract

As an extension of positive and almost positive diagrams and links, we study two classes of links we call successively almost positive and weakly successively almost positive links. We prove various properties of polynomial invariants and signatures of such links, extending previous results or answering open questions about positive or almost positive links. We discuss their minimal genus and fibering property and for the latter prove a fibering extension of Scharlemann-Thompson's theorem (valid for general links).