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

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