Knots and Coxeter Groups
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866913735915864064 |
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| author | Burke, Dylan Cuff-Chartrand, Geoffrey Espinosa, Malors Kazimierczak, Mateusz Mobedi, Mohammadamin |
| author_facet | Burke, Dylan Cuff-Chartrand, Geoffrey Espinosa, Malors Kazimierczak, Mateusz Mobedi, Mohammadamin |
| contents | In this paper we study knots created by galleries in the affine Coxeter complex of type \widewedge{B3}. We bound the stick number by 40 and prove that the smallest length of threefold rotationally symmetric trefoils is 42. We construct explicit galleries that knot as 9_35, 9_40, 9_41 and 9_47 in a way that has threefold rotational symmetry. We explain the construction of these galleries for 9_47 carefully. We conclude with three questions inspired by this work. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_10785 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Knots and Coxeter Groups Burke, Dylan Cuff-Chartrand, Geoffrey Espinosa, Malors Kazimierczak, Mateusz Mobedi, Mohammadamin Geometric Topology 57K10, 28A80 In this paper we study knots created by galleries in the affine Coxeter complex of type \widewedge{B3}. We bound the stick number by 40 and prove that the smallest length of threefold rotationally symmetric trefoils is 42. We construct explicit galleries that knot as 9_35, 9_40, 9_41 and 9_47 in a way that has threefold rotational symmetry. We explain the construction of these galleries for 9_47 carefully. We conclude with three questions inspired by this work. |
| title | Knots and Coxeter Groups |
| topic | Geometric Topology 57K10, 28A80 |
| url | https://arxiv.org/abs/2503.10785 |