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 $s \geq 2$, the higher topological complexity $TC_s$ of the unordered configuration spaces of trees $U\mathcal{C}^nT$, is maximal. In other words, we prove that, $TC_s(U \mathcal{C}^nT) = s(hdim (U \mathcal{C}^nT))$ where $hdim$ stands for the homotopy dimension.