The $L^2$-Alexander torsion is symmetric

TL;DR

This paper proves that the $L^2$-Alexander torsion of a 3-manifold exhibits symmetry, extending the known symmetry property of the Alexander polynomial of knots to a broader topological invariant.

Contribution

It establishes the symmetry of the $L^2$-Alexander torsion for 3-manifolds, generalizing the classical Alexander polynomial symmetry.

Findings

$L^2$-Alexander torsion is symmetric for 3-manifolds

Generalizes Alexander polynomial symmetry to $L^2$-torsion

Provides new insights into 3-manifold invariants

Abstract

We show that the $L^2$-Alexander torsion of a 3-manifold is symmetric. This can be viewed as a generalization of the symmetry of the Alexander polynomial of a knot.