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Twist spinning knotted trivalent graphs


Authors: J. Scott Carter and Seung Yeop Yang
Journal: Proc. Amer. Math. Soc. 144 (2016), 1371-1382
MSC (2010): Primary 57Q45
DOI: https://doi.org/10.1090/proc/12801
Published electronically: July 10, 2015
MathSciNet review: 3447687
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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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Additional Information

J. Scott Carter
Affiliation: Department of Mathematics, University of South Alabama, Mobile, Alabama 36688
Email: carter@southalabama.edu

Seung Yeop Yang
Affiliation: Department of Mathematics, The George Washington University, Washington, DC 20052
Email: syyang@gwu.edu

DOI: https://doi.org/10.1090/proc/12801
Received by editor(s): November 12, 2014
Received by editor(s) in revised form: March 17, 2015
Published electronically: July 10, 2015
Communicated by: Martin Scharlemann
Article copyright: © Copyright 2015 American Mathematical Society