Configuration spaces are not homotopy invariant

By Riccardo Longoni, Paolo Salvatore. 2004

81 citations recorded by the source corpus.

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.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/70edce7b35113cb56916128ec5bc2114735b05f3

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Geometry and Topology

1. David Ayala
2. J. Francis
3. M. Abouzaid
4. D. Auroux
5. I. Smith
6. Nick Sheridan
7. J. Pardon
8. Yankı Lekili

In Mathematical Physics

1. David Ayala
2. J. Francis
3. M. Abouzaid
4. D. Auroux
5. I. Smith
6. Nick Sheridan
7. J. Pardon
8. Yankı Lekili

Citations in the corpus

• Symplectic cohomology and Viterbo's theorem (2013, background): “In [17], Basu has extracted such an invariant, relying on the fact that the homotopy type of configuration spaces distinguishes the 3-dimensional lens spaces L(7, 1) and L(7, 2) [54].”
• Factorization homology of topological manifolds (2012, background): “The preceding result has as a consequence that factorization homology is not a homotopy invariant of a closed n-manifold, since the homotopy type of configuration spaces is known to be sensitive to simple homotopy equivalence by [28].”