论文标题
光滑功能的各节空间
The space of sections of a smooth function
论文作者
论文摘要
给定一个带边界的紧凑型歧管$ x $，$ f：x \ rightarrow y $的限制$ x $的边界具有孤立的关键点，其关键值不同，$ y $ as $ $ [0,1] $或$ s^1 $，$ f $ $ f $的连接组件的$ f $ $ fib $ f $ f $ f $ f $π_1$和π_1$。然后利用此计算为移动传感器网络的逃避路径问题的平滑版本提供新的结果：从覆盖区域的随时间变化的同源性以及边界共同体的随时间变化的杯赛，对于逃避路径的存在和较低的逃避路径类别的界限的必要条件。无需连接假设。
Given a compact manifold $X$ with boundary and a submersion $f : X \rightarrow Y$ whose restriction to the boundary of $X$ has isolated critical points with distinct critical values and where $Y$ is $[0,1]$ or $S^1$, the connected components of the space of sections of $f$ are computed from $π_0$ and $π_1$ of the fibers of $f$. This computation is then leveraged to provide new results on a smoothed version of the evasion path problem for mobile sensor networks: From the time-varying homology of the covered region and the time-varying cup-product on cohomology of the boundary, a necessary and sufficient condition for existence of an evasion path and a lower bound on the number of homotopy classes of evasion paths are computed. No connectivity assumptions are required.
