Divisibility conjecture for the Gornik invariants

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Let KK be a knot, and let sn(K)∈2Zs_n(K)\in 2\mathbb{Z} denote the even integer determined by the Gornik homology of KK for each n≥2n\geq 2. Divisibility conjecture for the Gornik invariants. For any knot KK and n≥2n\geq 2, one has

sn(K)∈2(n−1)Z.s_n(K)\in 2(n-1)\mathbb{Z}.

This is presented as a weaker conjecture than the proportionality conjecture relating the invariants sm(K)s_m(K) and sn(K)s_n(K). The source gives no resolution, so the conjecture remains open.

References

Primary source

Andrew Lobb, “A note on Gornik's perturbation of Khovanov-Rozansky homology”, arXiv:1012.2802 (2010).

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