Non-realizability of the spun Kishino knot

Let KIKI be the Kishino virtual knot, and let ST(KI)S_T(KI) denote its spun virtual 22-torus obtained by the construction ST(F×[0,1],K)=(F×S1×[0,1],K×S1)S_T(F\times [0,1],K)=(F\times S^1\times [0,1],K\times S^1). A virtual knot is realizable if it is represented by a classical knot. Spun Kishino non-realizability conjecture. ST(KI)S_T(KI) is not realizable. The preceding results show that ST(KI)S_T(KI) has the group and quandle of the unknot but a nontrivial biquandle; alternatively, it could represent a nonclassically realizable virtual knotted torus, so its realizability remains unresolved.

Sources & referencesView supporting material

Primary source

Blake Winter, “Virtual, Welded, and Ribbon Links in Arbitrary Dimensions”, arXiv:1407.0421 (2014).

Progress summary

Never refreshed

Nothing recorded yet. Refresh searches the literature and the public web for attempts on this problem, and writes the first summary here.

Solutions 0

No solutions have been posted yet.