1-loop equals torsion for fibered 3-manifolds

Understand

In earlier work of two of the authors, two 1-loop polynomial invariants of cusped 3-manifolds were constructed using combinatorial data of ideal triangulations, and conjectured to be equal to the $\mathbb{C}^2$ and the $\mathbb{C}^3$-torsion polynomials.

• Here, we prove this conjecture for layered triangulations of fibered 3-manifolds with toroidal boundary, and we illustrate our theorems with exact computations of the 1-loop and the torsion polynomials.
• As further evidence for the conjecture, we confirm it for more than 6,600 nonfibered manifolds, and use this data to explore the extent to which the $\mathbb{C}^2$-torsion determines the Thurston norm.