Twist spinning knotted trivalent graphs

J. Scott Carter; Seung Yeop Yang

doi:10.1090/proc/12801

Twist spinning knotted trivalent graphs

J. Scott Carter, Seung Yeop Yang

University of South Alabama

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

In 1965, E. C. Zeeman proved that the (±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 (±1)-twist spin of a knotted trivalent graph may be knotted. We then construct some families of knotted graphs for which the (±1)-twist spins are always unknotted.

Original language	English
Pages (from-to)	1371-1382
Number of pages	12
Journal	Proceedings of the American Mathematical Society
Volume	144
Issue number	3
DOIs	https://doi.org/10.1090/proc/12801
State	Published - Mar 2016

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abstract = "In 1965, E. C. Zeeman proved that the (±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{\textquoteright}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 (±1)-twist spin of a knotted trivalent graph may be knotted. We then construct some families of knotted graphs for which the (±1)-twist spins are always unknotted.",

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Twist spinning knotted trivalent graphs

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