Reduced universal character-ring conjecture for knot complements

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.

Sources & referencesView supporting material

Primary source

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

Progress summary

Never refreshed

Nothing recorded yet. Refresh searches the literature and the public web for attempts on this problem, and writes the first summary here.

Solutions 0

No solutions have been posted yet.