适当的拓扑复杂性

arXiv - MATH - Algebraic Topology Pub Date : 2024-07-23 DOI:arxiv-2407.16679

Jose M. Garcia-Calcines, Aniceto Murillo

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引用次数: 0

摘要

我们引入并研究了给定配置空间的适当拓扑复杂性，它是经典不变量的一个版本，我们要求控制运动的算法能够避免任何可能的 "不安全 "区域选择。为了使它成为同调函数式不变量，我们把它表征为外部映射的外部截面范畴的一个特殊实例，外部同调范畴的一个不变量也被深入分析了。

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Proper topological complexity

We introduce and study the proper topological complexity of a given configuration space, a version of the classical invariant for which we require that the algorithm controlling the motion is able to avoid any possible choice of ``unsafe'' area. To make it a homotopy functorial invariant we characterize it as a particular instance of the exterior sectional category of an exterior map, an invariant of the exterior homotopy category which is also deeply analyzed.

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arXiv - MATH - Algebraic Topology

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