论文标题
同型限制的逃避路径
Evasion paths by homotopy limits
论文作者
论文摘要
逃避路径问题询问何时可以导航动态变化的空间：例如，守卫正在巡逻一个地区，我们需要不在他们的视线之外。我们将Bousfield-Kan光谱序列用于同质逆极限，以计算逃避路径空间的同型组。这给出了我们称为``0段的空间''的路径数量（直至同喻的）的完整计算。我们给出了特征的此类空间，并通过根据覆盖区域对计算进行重新分配计算来得出结论。
The evasion paths problem asks when a dynamically changing space can be navigated: imagine guards are patrolling a region, for instance, and we need to stay outside their view. We use the Bousfield-Kan spectral sequence for homotopy inverse limits as a proxy for calculating the homotopy groups of the space of evasion paths. This gives a complete calculation of the number of paths (up to homotopy) for spaces we call ``0-sectional." We give a characterization such spaces, and conclude the paper by reframing the calculations in terms of the covered region.
