On the higher rational topological complexity of certain elliptic spaces

Abstract

Through this paper, we show that ${\text{TC}}_r(Z)\le r\cdot \text{cat}(Z)+{\chi }_{\pi }(Z)$, 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.