Self-dual Maps I : antipodality
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2020
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| _version_ | 1866910282575511552 |
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| author | Montejano, Luis Alfonsín, Jorge L. Ramírez Rasskin, Ivan |
| author_facet | Montejano, Luis Alfonsín, Jorge L. Ramírez Rasskin, Ivan |
| contents | A self-dual map $G$ is said to be \emph{antipodally self-dual} if the dual map $G^*$ is antipodal embedded in $\mathbb{S}^2$ with respect to $G$. In this paper, we investigate necessary and/or sufficient conditions for a map to be antipodally self-dual. In particular, we present a combinatorial characterization for map $G$ to be antipodally self-dual in terms of certain \emph{involutive labelings}. The latter lead us to obtain necessary conditions for a map to be \emph{strongly involutive} (a notion relevant for its connection with convex geometric problems). We also investigate the relation of antipodally self-dual maps and the notion of \emph{ antipodally symmetric} maps. It turns out that the latter is a very helpful tool to study questions concerning the \emph{symmetry} as well as the \emph{amphicheirality} of \emph{links}. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2008_12853 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Self-dual Maps I : antipodality Montejano, Luis Alfonsín, Jorge L. Ramírez Rasskin, Ivan Combinatorics A self-dual map $G$ is said to be \emph{antipodally self-dual} if the dual map $G^*$ is antipodal embedded in $\mathbb{S}^2$ with respect to $G$. In this paper, we investigate necessary and/or sufficient conditions for a map to be antipodally self-dual. In particular, we present a combinatorial characterization for map $G$ to be antipodally self-dual in terms of certain \emph{involutive labelings}. The latter lead us to obtain necessary conditions for a map to be \emph{strongly involutive} (a notion relevant for its connection with convex geometric problems). We also investigate the relation of antipodally self-dual maps and the notion of \emph{ antipodally symmetric} maps. It turns out that the latter is a very helpful tool to study questions concerning the \emph{symmetry} as well as the \emph{amphicheirality} of \emph{links}. |
| title | Self-dual Maps I : antipodality |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2008.12853 |