Year: 2026
Type: preprint
Abstract: We compare relative Abelian BF torsion with the Alexander-graded Euler characteristic of knot Floer homology. A meridional annulus boundary condition identifies the normalized relative torsion with the Alexander polynomial. One exact prime-cyclotomic torsion value recovers all its coefficients under a sharp genus bound, compatibly with connected-sum gluing and branched-cover formulas. We compute interface contractions and obstructions to scalar comparisons, including the pairing defect of two-sector reduction for the degree-zero torus algebra. A six-generator dg resolution yields an equivalence of perfect-module categories preserving derived pairings and admits a classical one-dimensional BV-BFV realization. In the fixed nonresonant polynomial quantum BFV sector, over characteristic zero with $\hbar$ inverted, both states and Weyl observables reduce to a vacuum field; a Hochschild invariant obstructs a Morita equivalence with the degree-zero torus algebra. These results do not establish a full geometric BV-BFV/Floer equivalence.
Source: arXiv (Cornell University)
Author: Moshayedi, Nima
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7223263891