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Configuration spaces are not homotopy invariant

2005; Elsevier BV; Volume: 44; Issue: 2 Linguagem: Inglês

10.1016/j.top.2004.11.002

1879-3215

Riccardo Longoni, Paolo Salvatore,

Algebraic structures and combinatorial models

We present a counterexample to the conjecture on the homotopy invariance of configuration spaces. More precisely, we consider the lens spaces L7,1 and L7,2, and prove that their configuration spaces are not homotopy equivalent by showing that their universal coverings have different Massey products.