Rank–torsion determination conjecture for prime knots

Let K1K_1 and K2K_2 be prime knots. Compare their ranks of Khovanov homology and their torsion subgroups.

Rank–torsion conjecture. The knots K1K_1 and K2K_2 have the same ranks of the Khovanov homology if and only if they have the same torsion.

The source calls this conjecture optimistic and says that its confirmation would be exciting because torsion may be easier to read from a diagram than the rest of the homology. No resolution status is given.

Sources & referencesView supporting material

Primary source

Alexander N. Shumakovitch, “Torsion of the Khovanov homology”, arXiv:math/0405474 (2018).

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