A generalization of several classical invariants of links

TL;DR

This paper generalizes classical link invariants such as linking number, Seifert form, Alexander module, polynomial, and signatures to links in quasi-cylinders, broadening their applicability beyond the 3-sphere.

Contribution

It introduces a unified framework extending key link invariants to the setting of quasi-cylinders, enabling new topological insights.

Findings

Classical invariants are successfully extended to quasi-cylinders.

The generalized invariants retain key properties of their classical counterparts.

This work opens avenues for studying links in more complex 3-manifolds.

Abstract

We extend several classical invariants of links in the 3-sphere to links in so-called quasi-cylinders. These invariants include the linking number, the Seifert form, the Alexander module, the Alexander-Conway polynomial and the Murasugi-Tristram-Levine signatures.