On the deleted squares of lens spaces

Kyle Evans-Lee, Nikolai Saveliev

Research output: Contribution to journalArticlepeer-review


The configuration space F2(M) of ordered pairs of distinct points in a manifold M, also known as the deleted square of M, is not a homotopy invariant of M: Longoni and Salvatore produced examples of homotopy equivalent lens spaces M and N of dimension three for which F2(M) and F2(N) are not homotopy equivalent. They also asked whether two arbitrary 3-dimensional lens spaces M and N must be homeomorphic in order for F2(M) and F2(N) to be homotopy equivalent. We give a partial answer to this question using a novel approach with the Cheeger-Simons differential characters.

Original languageEnglish (US)
Pages (from-to)134-152
Number of pages19
JournalTopology and its Applications
StatePublished - Aug 15 2016


  • Cheeger-Simons character
  • Chern-Simons invariant
  • Configuration space
  • Lens space

ASJC Scopus subject areas

  • Geometry and Topology


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