Twist spun knots of twist spun knots of classical knots
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866929482149920768 |
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| author | Fukuda, Mizuki Ishikawa, Masaharu |
| author_facet | Fukuda, Mizuki Ishikawa, Masaharu |
| contents | A $k$-twist spun knot is an $n+1$-dimensional knot in the $n+3$-dimensional sphere which is obtained from an $n$-dimensional knot in the $n+2$-dimensional sphere by applying an operation called a $k$-twist-spinning. This construction was introduced by Zeeman in 1965. In this paper, we show that the $m_2$-twist-spinning of the $m_1$-twist-spinning of a classical knot is a trivial $3$-knot in $S^5$ if $\gcd(m_1,m_2)=1$. We also give a sufficient condition for the $m_2$-twist-spinning of the $m_1$-twist-spinning of a classical knot to be non-trivial. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_00650 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Twist spun knots of twist spun knots of classical knots Fukuda, Mizuki Ishikawa, Masaharu Geometric Topology 57K45 (Primary) 57M05, 57M10, 57M60 (Secondary) A $k$-twist spun knot is an $n+1$-dimensional knot in the $n+3$-dimensional sphere which is obtained from an $n$-dimensional knot in the $n+2$-dimensional sphere by applying an operation called a $k$-twist-spinning. This construction was introduced by Zeeman in 1965. In this paper, we show that the $m_2$-twist-spinning of the $m_1$-twist-spinning of a classical knot is a trivial $3$-knot in $S^5$ if $\gcd(m_1,m_2)=1$. We also give a sufficient condition for the $m_2$-twist-spinning of the $m_1$-twist-spinning of a classical knot to be non-trivial. |
| title | Twist spun knots of twist spun knots of classical knots |
| topic | Geometric Topology 57K45 (Primary) 57M05, 57M10, 57M60 (Secondary) |
| url | https://arxiv.org/abs/2409.00650 |