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

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 str...

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Veröffentlicht in:	arXiv.org 2023-09
Hauptverfasser:	Hamoun, Said, Youssef Rami, Vandembroucq, Lucile
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Sprache:	eng
Schlagworte:	Upper bounds
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description	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 theorem for this type of models, which is actually our main result.
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title	An upper bound for the rational topological complexity of a family of elliptic spaces
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