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Regular-equivalence of 2-knot diagrams and sphere eversions

Published online by Cambridge University Press:  05 May 2016

MASAMICHI TAKASE  and
KOKORO TANAKA
MASAMICHI TAKASE
Affiliation:
Faculty of Science and Technology, Seikei University, 3-3-1 Kichijoji-kitamachi, Musashino, Tokyo 180-8633, Japan. e-mails: mtakase@st.seikei.ac.jp
KOKORO TANAKA
Affiliation:
Department of Mathematics, Tokyo Gakugei University, 4-1-1 Nukuikita-machi, Koganei, Tokyo 184-8501, Japan. e-mails: kotanaka@u-gakugei.ac.jp
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Abstract

For each diagram D of a 2-knot, we provide a way to construct a new diagram D′ of the same knot such that any sequence of Roseman moves between D and D′ necessarily involves branch points. The proof is done by developing the observation that no sphere eversion can be lifted to an isotopy in 4-space.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 161 , Issue 2 , September 2016 , pp. 237 - 246
Copyright
Copyright © Cambridge Philosophical Society 2016 

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References

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