Proves the Gang-Kim-Yoon integrality conjecture for adjoint Reidemeister torsions of all torus knots by defining Verlinde numbers via modular S-matrices and establishing their recursion formulas.
arXiv:2109.07058 , year=
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Proves algebraic integrality and local constancy of coefficients in twisted Alexander polynomials for torus knots under irreducible SL_n(C) representations, plus integrality of Reidemeister torsions for many Seifert fibered spaces.
The sum of adjoint Reidemeister torsions for twist knots is proven integral, with concrete generating function examples.
citing papers explorer
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Gang-Kim-Yoon integrality conjectures on adjoint Reidemeister torsions for torus knots
Proves the Gang-Kim-Yoon integrality conjecture for adjoint Reidemeister torsions of all torus knots by defining Verlinde numbers via modular S-matrices and establishing their recursion formulas.
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Algebraic properties of twisted Alexander polynomial and Reidemeister torsion of torus knots
Proves algebraic integrality and local constancy of coefficients in twisted Alexander polynomials for torus knots under irreducible SL_n(C) representations, plus integrality of Reidemeister torsions for many Seifert fibered spaces.
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Integrality of genus-$g$ indices with adjoint Reidemeister torsions of twist knots
The sum of adjoint Reidemeister torsions for twist knots is proven integral, with concrete generating function examples.