曲面的拓扑复杂性
Topological Complexities of Surfaces
摘要：
球面$S^2$和环面$T^2$是已知的唯一的具有较高拓扑复杂性的闭合连通曲面（对于每个$n\in\{2,3,...\}\subset\mathbb{N}$、$\mathrm{TC}_n(S^2)=n$和$\mathrm{TC}_n(T^2)=2n-2$）。本文的目的是找到大多数其他封闭连接曲面的拓扑复杂性。除了$S^2$，$T^2$，射影平面（$\mathbb{R}\mathbb{P}^2$）和Klein瓶外，所有的$n$和Klein瓶的拓扑复杂度都是$2n$ .
英文摘要：
The sphere $S^2$ and the torus $T^2$ are the only closed connected surfaces for which higher topological complexities are known (for each $n\in\{2,3,...\}\subset\mathbb{N}$, $\mathrm{TC}_n(S^2)=n$ and $\mathrm{TC}_n(T^2)=2n-2$). This text aims to find topological complexities for most other closed connected surfaces. For all but $S^2$, $T^2$, the projective plane ($\mathbb{R}\mathbb{P}^2$) and the Klein bottle the $n$-th topological complexity is $2n$.
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。
