Finite-rank conjecture for atoroidal 3-manifold skein modules

Let MM be an oriented atoroidal 33-manifold, and let S2,(M)\mathcal{S}_{2,\infty}(M) denote its Kauffman bracket skein module. Finite-rank conjecture. The Kauffman bracket skein module S2,(M)\mathcal{S}_{2,\infty}(M) of oriented atoroidal 33-manifolds has finite rank. This conjecture is presented as a consequence of combining the torsion characterization conjecture with Witten's finite-dimensionality conjecture; the supplied text gives no proof or resolution.

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Primary source

Rhea Palak Bakshi, Dionne Ibarra, Gabriel Montoya-Vega, Józef H. Przytycki and Deborah Weeks, “On framings of links in 3-manifolds”, arXiv:2001.07782 (2023).

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