Bounds for the higher topological complexity of configuration spaces of trees

Abstract

For a tree $T$, we show that for many positive integer values of $n$, and an integer $s\ge 2$, the higher topological complexity $T{C}_s$ of the unordered configuration spaces of trees $U{\mathcal{C}}^{n}T$, is maximal. In other words, we prove that, $T{C}_s(U{\mathcal{C}}^{n}T)=s(hdim(U{\mathcal{C}}^{n}T))$ where $hdim$ stands for the homotopy dimension.

arXiv comment12 pages, 4 figures