Torsion conjecture for Kauffman bracket skein modules of connected sums

Let M=M1#M2M=M_1\# M_2, where each MiM_i is a 3-manifold, possibly with holes, and neither MiM_i is equal to S3S^3. Let S2,(M){\cal S}_{2,\infty}(M) denote the Kauffman bracket skein module of MM. Connected-sum torsion conjecture. The module S2,(M){\cal S}_{2,\infty}(M) has a torsion element. This conjecture concerns torsion beyond the established torsion arising from a non-separating S2S^2; its status is open.

Sources & referencesView supporting material

Primary source

Jozef H. Przytycki, “Skein modules”, arXiv:math/0602264 (2006).

Additional references

2 papers in this index state this conjecture (1998–2006). The statement above is taken from the most recent of them; the others are arXiv:math/9809113.

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