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In this work, we show that, for any simply-connected elliptic space $S$admitting a pure minimal Sullivan model with a differential of constant length,we have ${\rm TC}_0(S)\leq 2{\rm cat}_0(S)+\chi_{\pi}(S)$ where $\chi_{\pi}(S)$is the homotopy characteristic. This is a consequence of a structure theoremfor this type of models, which is actually our main result.

An upper bound for the rational topological complexity of a family of elliptic spaces