On the deleted squares of lens spaces

Kyle Evans-Lee, Nikolai Saveliev

Research output: Contribution to journalArticle

Abstract

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
Volume209
DOIs
StatePublished - Aug 15 2016

Fingerprint

Lens Space
Homotopy
Ordered pair
Homeomorphic
Configuration Space
Three-dimension
Distinct
Partial
Invariant
Arbitrary

Keywords

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

ASJC Scopus subject areas

  • Geometry and Topology

Cite this

On the deleted squares of lens spaces. / Evans-Lee, Kyle; Saveliev, Nikolai.

In: Topology and its Applications, Vol. 209, 15.08.2016, p. 134-152.

Research output: Contribution to journalArticle

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