The topological complexity of a path-connected space , denoted by , can be thought of as the minimum number of continuous rules needed to describe how to move from one point in to another. The space is often interpreted as a configuration space in some real-life context. Here, we consider the case where is the space of configurations of points on a tree . We will be interested in two such configuration spaces. In the first, denoted by , the points are distinguishable, while in the second, , the points are indistinguishable. We determine for any tree and many values of , and consequently determine for the same values of (provided the configuration spaces are path-connected).
"Topological complexity of $n$ points on a tree." Algebr. Geom. Topol. 18 (2) 839 - 876, 2018. https://doi.org/10.2140/agt.2018.18.839