1-loop equals torsion for fibered 3-manifolds

2023/04/02 by Dunfield, Nathan M., Stavros Garoufalidis, Garoufalidis, Stavros +2 · 1 citation
Computer Science · Mathematics · #57K31 #57K32 #Advanced Combinatorial Mathematics #FOS: Mathematics #FOS: Physical sciences #Geometric Topology (math.GT) #Geometric and Algebraic Topology #High Energy Physics - Theory (hep-th) #Topological and Geometric Data Analysis

paper · pdf · doi:10.48550/arxiv.2304.00469

openalex publication_date 2023/04/02 · openalex created_date 2023/04/06 · openalex updated_date 2026/07/28

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 ℂ² and the ℂ³-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 ℂ²-torsion determines the Thurston norm.

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• The complete 10-tetrahedra census of orientable cusped hyperbolic 3-manifolds

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