Gluing formulas for the $L^2$-Alexander torsions

TL;DR

This paper establishes new gluing formulas for the $L^2$-Alexander torsions of links, including explicit computations for torus links in various 3-manifolds, advancing the understanding of link invariants.

Contribution

It introduces Torres-like and other formulas for $L^2$-Alexander torsions, with explicit calculations for specific link types, expanding the computational toolkit for link invariants.

Findings

Derived Torres-like formula for $L^2$-Alexander torsions

Formulas for connected sums and cablings of links

Explicit computations for torus links in different 3-manifolds

Abstract

We prove a Torres-like formula for the $L^2$-Alexander torsions of links, as well as formulas for connected sums and cablings of links. Along the way we compute explicitly the $L^2$-Alexander torsions of torus links inside the three-sphere, the solid torus and the thickened torus.