Isolated regions of a link projection
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866914965070282752 |
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| author | Mahato, Tumpa Shimizu, Ayaka |
| author_facet | Mahato, Tumpa Shimizu, Ayaka |
| contents | A set of regions of a link projection is said to be isolated if any pair of regions in the set share no crossings. The isolate-region number of a link projection is the maximum value of the cardinality for isolated sets of regions of the link projection. In this paper, all the link projections of isolate-region number one are determined. Also, estimations for welded unknotting number and combinatorial way to find the isolate-region number are discussed, and a formula of the generating function of isolated-region sets is given for the standard projections of $(2, n)$-torus links. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_15818 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Isolated regions of a link projection Mahato, Tumpa Shimizu, Ayaka Geometric Topology A set of regions of a link projection is said to be isolated if any pair of regions in the set share no crossings. The isolate-region number of a link projection is the maximum value of the cardinality for isolated sets of regions of the link projection. In this paper, all the link projections of isolate-region number one are determined. Also, estimations for welded unknotting number and combinatorial way to find the isolate-region number are discussed, and a formula of the generating function of isolated-region sets is given for the standard projections of $(2, n)$-torus links. |
| title | Isolated regions of a link projection |
| topic | Geometric Topology |
| url | https://arxiv.org/abs/2404.15818 |