Configuration spaces are not homotopy invariant

Details Configuration spaces are not homotopy invariant Configuration spaces are not homotopy invariant

2004-01-08

arxiv.org/abs/math/0401075v1

Mathematics

Algebraic Topology

6 pages

Scientific paper

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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