TWIST-SPUN KNOTS OF TWIST-SPUN KNOTS OF CLASSICAL KNOTS
A k-twist-spun knot is an (n+1)-dimensional knot in the (n+3)-dimensional sphere that 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 (1965). In this paper, we show that the m2-twis...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Dalat University
2025-05-01
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| Series: | Tạp chí Khoa học Đại học Đà Lạt |
| Subjects: | |
| Online Access: | https://tckh.dlu.edu.vn/index.php/tckhdhdl/article/view/1444 |
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| Summary: | A k-twist-spun knot is an (n+1)-dimensional knot in the (n+3)-dimensional sphere that 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 (1965). In this paper, we show that the m2-twist-spinning of the m1-twist-spinning of a classical knot is a trivial 3-knot in S5 if gcd(m1, m2) = 1. We also give a sufficient condition for the m2-twist-spinning of the m1-twist-spinning of a classical knot to be nontrivial.
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| ISSN: | 0866-787X |