Conjecture on free and torsion decompositions of Kauffman bracket skein modules

Let MM be a closed, oriented 33-manifold, and let S(M)\mathscr S(M) denote its Kauffman bracket skein module over Z[A±1]\mathbb Z[A^{\pm1}]. A module decomposition into free modules and torsion modules means a direct-sum decomposition of that form. Free–torsion decomposition conjecture.

  1. The Kauffman bracket skein module of any closed, prime, oriented 33-manifold over Z[A±1]\mathbb Z[A^{\pm1}] can be decomposed into the direct sum of free modules and torsion modules.
  2. The Kauffman bracket skein module of any non-prime, oriented 33-manifold over Z[A±1]\mathbb Z[A^{\pm1}] cannot be decomposed into the direct sum of free modules and torsion modules.

The supplied text attributes this two-part claim to prior work and gives no evidence resolving either assertion, so both remain open here.

References

Primary source

Rhea Palak Bakshi, Thang T. Q. Lê and Józef H. Przytycki, “Kauffman bracket skein module of the connected sum of two solid tori”, arXiv:2604.09971 (2026).

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.