Heawood 族的拓扑对称性
Topological Symmetries of the Heawood family
AI总结：
本文研究 Heawood 族图在 S³ 中的拓扑对称群，完整确定各图可实现的对称群，并据此证明该族所有图均为本征手性。
摘要：
抽象图 γ 在 S³ 中的嵌入 Γ 的拓扑对称群，是指可由空间对 (S³, Γ) 的同胚实现的 γ 自同构所组成的群。这类群的研究动机来自关于空间中分子对称性的问题。本文找出了可作为 Heawood 族中每一个图的拓扑对称群而实现的所有群。Heawood 族是一类重要的空间图集合，包含了边数不超过 21 的唯一本征纽结图。作为推论，我们发现该族中的所有图都是本征手性的。
英文摘要：
The {\em topological symmetry group} of an embedding $Γ$ of an abstract graph $γ$ in $S^3$ is the group of automorphisms of $γ$ which can be realized by homeomorphisms of the pair $(S^3, Γ)$. These groups are motivated by questions about the symmetries of molecules in space. In this paper, we find all the groups which can be realized as topological symmetry groups for each of the graphs in the Heawood family. This is an important collection of spatial graphs, containing the only intrinsically knotted graphs with 21 or fewer edges. As a consequence, we discover that the graphs in this family are all intrinsically chiral.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
