Conjecture on knot Floer homology of prime fibered positive knots
Conjecture on knot Floer homology of prime fibered positive knots
Let be a prime fibered positive knot of genus , and let denote its knot Floer homology in Alexander grading and Maslov grading , with coefficients in . The knot Floer homology conjecture.
This conjecture is motivated by computations for prime fibered positive knots with at most 14 crossings and by constraints from the Kauffman state model. Whether the assertion holds for all prime fibered positive knots remains open.
Sources & referencesView supporting material
Primary source
Zhechi Cheng and Matthew Hedden, “Knot Floer homology of positive braids”, arXiv:2504.13005 (2026).
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