The Adjoint Reidemeister Torsion for Compact 3-Manifolds Admit a Unique Decomposition

TL;DR

This paper proves that the adjoint Reidemeister torsion exhibits a multiplicative property under the unique disk sum decomposition of compact 3-manifolds, simplifying calculations in topological invariants.

Contribution

It establishes the multiplicative behavior of the adjoint Reidemeister torsion for 3-manifolds decomposed into prime components, without additional correction factors.

Findings

Reidemeister torsion is multiplicative under disk sum decomposition.

Unique prime decomposition of 3-manifolds influences torsion calculation.

No corrective term needed for the torsion's multiplicativity.

Abstract

Let $M$ be a triangulated, oriented, connected compact $3$-manifold with connected non-empty boundary. Such a manifold admits a unique decomposition into $\triangle$-prime $3$-manifolds. In this paper, we show that the adjoint Reidemeister torsion has a multiplicative property on the disk sum decomposition of compact $3$-manifolds without a corrective term.