Rank–torsion determination conjecture for prime knots
Rank–torsion determination conjecture for prime knots
Let and be prime knots. Compare their ranks of Khovanov homology and their torsion subgroups.
Rank–torsion conjecture. The knots and 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).
Progress summary
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