Reduced universal character-ring conjecture for knot complements

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For a knot KK, let XX be its complement and let Cuniv[χ(X)]\mathbb C^{\mathrm{univ}}[\chi(X)] denote the universal SL2SL_2-character ring of π1(X)\pi_1(X), equivalently the skein module at t=−1t=-1 under the stated identification. A ring is reduced when its nilradical is zero. Reduced universal character-ring conjecture. For every knot KK, the universal SL2SL_2-character ring is reduced. If true, this would identify the universal character ring with the coordinate ring of the SL2SL_2-character variety for every knot complement; the supplied context lists several classes where reducedness is already known, but gives no resolution in general.

References

Primary source

Thang T. Q. Le and Anh T. Tran, “On the AJ conjecture for knots”, arXiv:1111.5258 (2014).

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