Topological Classification of Defects in Ordered Media

Abstract

In this thesis, defects in ordered media will be introduced. Then, they will be classified, first introducing a physical measure of equivalence, and then translating that to mathematics via homotopy theory. It will turn out that point defects in $\bR^2$ and line defects in $\bR^3$ are classified by conjugacy classes of the fundamental group. Finally, after some examples of defects, a relatively simple way to compute the fundamental group is discussed.