Cyclic Covering Spaces of Knot Complements

Mark Flanagan

Date of Award

2008

Document Type

Thesis

Degree Name

Bachelors

Department

Natural Sciences

First Advisor

Mullins, David

Keywords

Knots, Covering Spaces, Algebraic Topology

Area of Concentration

Mathematics

Abstract

Covering spaces comprise important classes of knot invariants. The purpose of this expository thesis is to provide an introduction to the study of classical knots that focuses on the construction of cyclic covering invariants. First we will introduce knots, with a discussion of knot equivalence and invariants. Then, after developing the necessary homotopy theory, we construct cyclic covering spaces of knot complements using Seifert surfaces. This allows us to define the Alexander polynomial of a knot � a powerful knot invariant. We conclude the thesis with a theorem that relates the Alexander polynomial to the order of the first homology of cyclic branched covers of the three-sphere.

Rights

This bibliographic record is available under the Creative Commons CC0 public domain dedication. The New College of Florida, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.

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