Regular-equivalence of $2$-knot diagrams and sphere eversions

Masamichi Takase; Kokoro Tanaka

doi:10.1017/s0305004116000244

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arXiv · 1406.3539

Regular-equivalence of $2$-knot diagrams and sphere eversions

Masamichi Takase·Kokoro Tanaka

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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.

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BibTeX RIS

Masamichi Takase, Kokoro Tanaka. 2014-06-13. Regular-equivalence of $2$-knot diagrams and sphere eversions. https://doi.org/10.1017/s0305004116000244

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