Ball packings for links
Fuente:
arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2020
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| _version_ | 1866910282589143040 |
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| author | Alfonsín, Jorge Luis Ramírez Rasskin, Ivan |
| author_facet | Alfonsín, Jorge Luis Ramírez Rasskin, Ivan |
| contents | The ball number of a link $L$, denoted by $ball(L)$, is the minimum number of solid balls (not necessarily of the same size) needed to realize a necklace representing $L$. In this paper, we show that $ball(L)\leq 5 cr(L)$ where $cr(L)$ denotes the crossing number of $L$. To this end, we use Lorentz geometry applied to ball packings. The well-known Koebe-Andreev-Thurston circle packing Theorem is also an important brick for the proof. Our approach yields to an algorithm to construct explicitly the desired necklace representation of $L$ in the 3-dimensional space. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2010_00580 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Ball packings for links Alfonsín, Jorge Luis Ramírez Rasskin, Ivan Combinatorics Geometric Topology 52C17, 57K10 The ball number of a link $L$, denoted by $ball(L)$, is the minimum number of solid balls (not necessarily of the same size) needed to realize a necklace representing $L$. In this paper, we show that $ball(L)\leq 5 cr(L)$ where $cr(L)$ denotes the crossing number of $L$. To this end, we use Lorentz geometry applied to ball packings. The well-known Koebe-Andreev-Thurston circle packing Theorem is also an important brick for the proof. Our approach yields to an algorithm to construct explicitly the desired necklace representation of $L$ in the 3-dimensional space. |
| title | Ball packings for links |
| topic | Combinatorics Geometric Topology 52C17, 57K10 |
| url | https://arxiv.org/abs/2010.00580 |