Ultraknots and limit knots
Fuente:
arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866909079112253440 |
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| author | Bode, Benjamin |
| author_facet | Bode, Benjamin |
| contents | We prove that every knot type in $\mathbb{R}^3$ can be parametrised by a smooth function $f:S^1\to\mathbb{R}^3$, $f(t)=(x(t),y(t),z(t))$ such that all derivatives $f^{(n)}(t)=(x^{(n)}(t),y^{(n)}(t),z^{(n)}(t))$, $n\in\mathbb{N}$, parametrise knots and every knot type appears in the corresponding sequence of knots. We also study knot types that arise as limits of such sequences. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_11918 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Ultraknots and limit knots Bode, Benjamin Geometric Topology We prove that every knot type in $\mathbb{R}^3$ can be parametrised by a smooth function $f:S^1\to\mathbb{R}^3$, $f(t)=(x(t),y(t),z(t))$ such that all derivatives $f^{(n)}(t)=(x^{(n)}(t),y^{(n)}(t),z^{(n)}(t))$, $n\in\mathbb{N}$, parametrise knots and every knot type appears in the corresponding sequence of knots. We also study knot types that arise as limits of such sequences. |
| title | Ultraknots and limit knots |
| topic | Geometric Topology |
| url | https://arxiv.org/abs/2401.11918 |