On the deleted squares of lens spaces

2015/02/11 by Kyle Evans-Lee, Evans-Lee, Kyle, Nikolai Saveliev +1
Mathematics · #55R80 #55S30 #57M27 #57R19 #Algebraic Topology (math.AT) #FOS: Mathematics #Geometric Topology (math.GT) #math.AT #math.GT #msc:55R80 #msc:55S30 #msc:57M27 #msc:57R19

paper · pdf · doi:10.48550/arxiv.1502.03408

27 pages, 10 figures

arxiv created 2015/02/11 · arxiv updated 2015/02/12

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. In this paper, we study the natural question 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. Among our tools are the Cheeger--Simons differential characters of deleted squares and the Massey products of their universal covers.

Related

• Configuration spaces are not homotopy invariant
• Lens spaces given from L-space homology 3-spheres
• Lens space surgeries and L-space homology spheres
• Two Representations of the Fundamential Group and Invariants of Lens Spaces
• The Smale Conjecture for lens spaces