Turaev Torsion Invariants of 3-orbifolds

TL;DR

This paper introduces a new combinatorial invariant for 3-orbifolds with link singularities, extending Turaev torsion invariants from 3-manifolds, and provides formulas describing how this invariant changes under modifications.

Contribution

It generalizes Turaev torsion invariants to 3-orbifolds with singular links and derives formulas for how the invariant varies with modifications of the singular set.

Findings

Derived gluing formulas for the invariant

Established relationship between orbifold and manifold invariants

Analyzed the effect of removing singular components

Abstract

We construct a combinatorial invariant of 3-orbifolds with singular set a link that generalizes the Turaev torsion invariant of 3-manifolds. We give several gluing formulas from which we derive two consequences. The first is an understanding of how the components of the invariant change when we remove a curve from the singular set. The second is a formula relating the invariant of the 3-orbifold to the Turaev torsion invariant of the underlying 3-manifold in the case when the singular set is a nullhomologous knot.