Doctor of Philosophy (PHD)
Mathematics (Arts and Sciences)
Date of Defense
First Committee Member
Second Committee Member
Third Committee Member
Fourth Committee Member
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. 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, Massey products of their universal covers, and the Reidemeister torsion of compactified deleted squares.
Configuration Space; Lens Spaces; Chern-Simons; Massey Product
Evans-Lee, Kyle H., "On the Configuration Spaces of Lens Spaces" (2015). Open Access Dissertations. 1413.