Vanishing of the virtual Alexander polynomial for slice virtual knots

From papers

Let KK be a virtual knot, and let HK(s,t,q)H_K(s,t,q) denote its virtual Alexander polynomial.

Vanishing conjecture. If KK is slice, then

HK(s,t,q)=0.H_K(s,t,q)=0.

The polynomial was introduced as a slice obstruction, and it vanishes for all slice virtual knots currently known. Whether it vanishes for every slice virtual knot, and whether it is a concordance invariant, remains open.

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Sources & referencesView supporting material

Primary source

Hans U. Boden, Micah Chrisman and Robin Gaudreau, “Virtual knot cobordism and bounding the slice genus”, arXiv:1708.05982 (2017).

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