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PreprintCC BY 4.0arXiv

Alexander Torsion and Floer Comparisons in the BV-BFV Formalism

  • Nima Moshayedi
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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 ℏ 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.

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Cite

BibTeXRIS
BibTeX
@misc{moshayedi2026alexander,
  title = {{Alexander Torsion and Floer Comparisons in the BV-BFV Formalism}},
  author = {Nima Moshayedi},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.30192},
  eprint = {2610.30192},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.30192},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Alexander Torsion and Floer Comparisons in the BV-BFV Formalism
AU  - Nima Moshayedi
PY  - 2026
DA  - 2026/10/21
PB  - arXiv
DO  - 10.48550/arxiv.2610.30192
UR  - https://arxiv.org/abs/2610.30192
AB  - 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 ℏ 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.
ER  -