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Configuration spaces are not homotopy invariant

Riccardo Longoni·Paolo Salvatore
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Abstract

We present a counterexample to the conjecture on the homotopy invariance of configuration spaces. More precisely, we consider the lens spaces $L_{7,1}$ and $L_{7,2}$, and prove that their configuration spaces are not homotopy equivalent by showing that their universal coverings have different Massey products.

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Riccardo Longoni, Paolo Salvatore. 2004-01-08. Configuration spaces are not homotopy invariant. https://arxiv.org/abs/math/0401075

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