Glasses: A suitable case for homotopy?

Abstract

In reply to a recent paper by Steinhardt and Chaudhari (1981), it is argued that glasses can be described by a field theory in continuous space, upon which the identification and classification of topologically stable defects can be made by homotopy theory. Overall homogeneity of glasses is expressed as a local, or gauge invariance, and gauge fields establish a connection between different points in the glass. The only topologically stable defects in glasses are odd line defects or 'disclinations'.