On higher analogs of topological complexity

Farber introduced a notion of topological complexity $\text{TC}(X)$ that is related to robotics. Here we introduce a series of numerical invariants $\TC_n(X), n=1,2, …$suchthat$\TC_2(X)=\TC(X)$and$\TC_n(X)\le \TC_{n+1}(X)$. For these higher complexities, we define their symmetric versions that can also be regarded as higher analogs of the symmetric topological complexity.