Publication Date
2015-04-29
Availability
Open access
Embargo Period
2015-04-29
Degree Type
Dissertation
Degree Name
Doctor of Philosophy (PHD)
Department
Mathematics (Arts and Sciences)
Date of Defense
2015-04-02
First Committee Member
Nikolai Saveliev
Second Committee Member
Kenneth Baker
Third Committee Member
Alexander Dvorsky
Fourth Committee Member
Rafael Nepomechie
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. 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.
Keywords
Configuration Space; Lens Spaces; Chern-Simons; Massey Product
Recommended Citation
Evans-Lee, Kyle H., "On the Configuration Spaces of Lens Spaces" (2015). Open Access Dissertations. 1413.
https://scholarlyrepository.miami.edu/oa_dissertations/1413