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| Main Author: | |
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| Format: | Preprint |
| Published: |
2021
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2105.08634 |
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| _version_ | 1866916208750624768 |
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| author | Yasuda, Jumpei |
| author_facet | Yasuda, Jumpei |
| contents | In this paper, we introduce a method, called a plat form, of describing a surface-link in the 4-space using a braided surface. We prove that every surface-link, which is not necessarily orientable, can be described in a plat form. The plat index is defined as a surface-link invariant, which is an analogy of the bridge index for a link in the 3-space. We classify surface-links with plat index $1$ and show some examples of surface-links in plat forms. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2105_08634 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | A plat form presentation for surface-links Yasuda, Jumpei Geometric Topology 57K45, 57K10 In this paper, we introduce a method, called a plat form, of describing a surface-link in the 4-space using a braided surface. We prove that every surface-link, which is not necessarily orientable, can be described in a plat form. The plat index is defined as a surface-link invariant, which is an analogy of the bridge index for a link in the 3-space. We classify surface-links with plat index $1$ and show some examples of surface-links in plat forms. |
| title | A plat form presentation for surface-links |
| topic | Geometric Topology 57K45, 57K10 |
| url | https://arxiv.org/abs/2105.08634 |