运动规划的Lusternik-Schnirelmann范畴与基于基点的拓扑复杂度
代数拓扑
2015-08-20 v2
摘要
Farber和Rudyak引入了运动规划的拓扑复杂度及其高阶类似物来衡量为点元组分配路径的复杂度。受到运动规划的启发，其中机器人系统从初始构型出发，在经过一系列位置列表后可能返回，我们定义了三类其他拓扑复杂度、和。我们将比较这些概念，并对一些熟悉的空间类别计算后者的值。
引用
@article{arxiv.1508.04209,
title = {Lusternik-Schnirelmann category and based topological complexities of motion planning},
author = {Yongheng Zhang},
journal= {arXiv preprint arXiv:1508.04209},
year = {2015}
}
备注
7 pages; comments added: LTC_2(X) was introduced earlier by My Ismail Mamouni and Derfoufi Younes and they concluded that LTC_2(X)=TC(X)