Shadows of 2-knots and complexity
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2022
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| _version_ | 1866916540548382720 |
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| author | Naoe, Hironobu |
| author_facet | Naoe, Hironobu |
| contents | We introduce a new invariant for a $2$-knot in $S^4$, called the shadow-complexity, based on the theory of Turaev shadows, and we give a characterization of $2$-knots with shadow-complexity at most $1$. Specifically, we show that the unknot is the only $2$-knot with shadow-complexity $0$ and that there exist infinitely many $2$-knots with shadow-complexity $1$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2208_09173 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Shadows of 2-knots and complexity Naoe, Hironobu Geometric Topology 57K45 (Primary), 57R65 (Secondary) We introduce a new invariant for a $2$-knot in $S^4$, called the shadow-complexity, based on the theory of Turaev shadows, and we give a characterization of $2$-knots with shadow-complexity at most $1$. Specifically, we show that the unknot is the only $2$-knot with shadow-complexity $0$ and that there exist infinitely many $2$-knots with shadow-complexity $1$. |
| title | Shadows of 2-knots and complexity |
| topic | Geometric Topology 57K45 (Primary), 57R65 (Secondary) |
| url | https://arxiv.org/abs/2208.09173 |