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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2303.14503 |
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| _version_ | 1866909630586683392 |
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| author | Garaev, T. R. |
| author_facet | Garaev, T. R. |
| contents | Let $K$ be the graph on vertices $\{1, 2, 3, 4, 5\}$, and having all edges except $(4, 5)$. A continuous map $f:K\to \R^2$ is called an \emph{almost embedding} if $f$-images of non-adjacent edges are disjoint. Take the winding numbers of the $f$-image of the oriented cycle $(1, 2, 3)$ around $f(4)$ and around $f(5)$. We prove that the difference of these numbers equals $\pm 1$. This is surprising, because in other similar situations analogous statement is wrong. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2303_14503 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On winding numbers of $K_5$ minus an edge in the plane Garaev, T. R. Combinatorics Geometric Topology Let $K$ be the graph on vertices $\{1, 2, 3, 4, 5\}$, and having all edges except $(4, 5)$. A continuous map $f:K\to \R^2$ is called an \emph{almost embedding} if $f$-images of non-adjacent edges are disjoint. Take the winding numbers of the $f$-image of the oriented cycle $(1, 2, 3)$ around $f(4)$ and around $f(5)$. We prove that the difference of these numbers equals $\pm 1$. This is surprising, because in other similar situations analogous statement is wrong. |
| title | On winding numbers of $K_5$ minus an edge in the plane |
| topic | Combinatorics Geometric Topology |
| url | https://arxiv.org/abs/2303.14503 |