Unknotting submanifolds of the 3-sphere by twistings

Makoto Ozawa

記述言語: 英語
掲載種別
DOI: 10.2422/2036-2145.201612_007

By the Fox's re-embedding theorem, any compact submanifold of the 3-sphere
can be re-embedded in the 3-sphere so that it is unknotted. It is unknown
whether the Fox's re-embedding can be replaced with twistings. In this paper,
we will show that any closed 2-manifold embedded in the 3-sphere can be
unknotted by twistings. In spite of this phenomenon, we show that there exists
a compact 3-submanifold of the 3-sphere which cannot be unknotted by twistings.
This shows that the Fox's re-embedding cannot always be replaced with
twistings.

リンク情報

DOI: https://doi.org/10.2422/2036-2145.201612_007
arXiv: http://arxiv.org/abs/arXiv:1609.06573
Arxiv Url: http://arxiv.org/abs/1609.06573v3
Arxiv Url: http://arxiv.org/pdf/1609.06573v3 本文へのリンクあり

ID情報

DOI : 10.2422/2036-2145.201612_007
arXiv ID : arXiv:1609.06573

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Unknotting submanifolds of the 3-sphere by twistings

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