The homotopy groups of condensed matter physics

Abstract

The classes of distinct point and line defects in ordered media and the laws governing their combination, are determined by the fundamental group of the order parameter space π1, the second homotopy group π2, and the group of automorphisms induced in π2 by the action of π1. A simple algorithm is given for computing all of these algebraic structures for a quite general family of ordered forms of condensed matter.