论文标题
自动偶像地图I：反技术
Self-dual Maps I : antipodality
论文作者
论文摘要
如果双映射$ g^*$相对于$ g $，则据说是\ emph {antipodally self-dual}的自偶型地图$ g $。在本文中，我们调查了地图具有反应自我为偶的必要和/或足够条件。特别是，我们提出了MAP $ G $的组合表征，以某些\ emph {涉及标签}的形式进行反应自我划。后者导致我们获得了将映射为\ emph {强涉及}的必要条件（与凸几何问题有关的概念）。我们还研究了反式自偶像图的关系和\ emph {antipodally对称}地图的概念。事实证明，后者是研究有关\ emph {对称性}的问题以及\ emph {links}的\ emph {amphicheirality}的非常有用的工具。
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}.
