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1-loop equals torsion for fibered 3-manifolds
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abstract
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.
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Adjoint Reidemeister torsion of 3-manifolds with torus boundary for semisimple algebraic groups
Adjoint Reidemeister torsion is defined for semisimple algebraic groups on 3-manifolds with torus boundary, and for hyperbolic manifolds it factors through principal PGL2 embeddings into products of known PGL2 torsions.
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