On the higher rational topological complexity of certain elliptic spaces

Abstract: Through this paper, we show that $\text{TC}r(Z)\leq r\cdot \text{cat}(Z)+\chi{\pi}(Z)$, for any simply-connected elliptic space $Z$ admitting a pure minimal Sullivan model with a differential of constant length. Here $\chi_{\pi}(Z)$ denotes the homotopy characteristic and $r$ is an integer greater or equals than $2$. We also give a lower bound for $\text{TC}_r$ in the framework of coformal spaces and we compute the exact value of $\text{TC}_r$ for certain families of spaces.