Twist spinning knotted trivalent graphs

Carter, J.; Yang, Seung

doi:10.1090/proc/12801

Twist spinning knotted trivalent graphs
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by J. Scott Carter and Seung Yeop Yang PDF

Proc. Amer. Math. Soc. 144 (2016), 1371-1382 Request permission

Abstract:

In 1965, E. C. Zeeman proved that the $(\pm 1)$-twist spin of any knotted sphere in $(n-1)$-space is unknotted in the $n$-sphere. In 1991, Y. Marumoto and Y. Nakanishi gave an alternate proof of Zeeman’s theorem by using the moving picture method. In this paper, we define a knotted $2$-dimensional foam which is a generalization of a knotted sphere and prove that a $(\pm 1)$-twist spin of a knotted trivalent graph may be knotted. We then construct some families of knotted graphs for which the $(\pm 1)$-twist spins are always unknotted.

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