Versal unfolding

Summary

An unfolding of a function germ is a family of germs depending on parameters that reduces to the given germ when the parameters are zero. An unfolding is versal if every other unfolding can be obtained from it by changes of a simple kind. These are a change of parameters, a parameter-dependent change of coordinates and the addition of a function of the parameters. So a versal unfolding contains, up to equivalence, every way of perturbing the germ. A versal unfolding with the least number of parameters is called universal or miniversal, and that number is the codimension of the germ. Versal unfoldings are the normal forms of catastrophe theory.