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

TL;DR

This paper establishes an upper bound for the rational topological complexity of certain elliptic spaces using their minimal Sullivan models and homotopy invariants, advancing understanding in algebraic topology.

Contribution

It provides a new upper bound for the rational topological complexity of elliptic spaces with pure minimal Sullivan models, based on their homotopy characteristic.

Findings

Derived an upper bound: TC_0(S) ≤ 2 cat_0(S) + χ_π(S)

Proved a structure theorem for pure minimal Sullivan models

Connected algebraic models to topological complexity measures

Abstract

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.