Topological defects

An idealized vortex in a 2D fluid involves velocity vectors that in effect wind around a point—and can never be unwound by making a series of small local perturbations. The result is a certain kind of stability that can be viewed as being of topological origin. One can classify forms of stability like this in terms of the mathematics of homotopy. Most common are point and line defects in vector fields, but more complicated defects can occur, notably in liquid crystals, models of condensates in the early universe, and certain nonlinear field theories. Analogs of homotopy can presumably be devised to represent certain forms of stability in systems like the networks I consider.