Geometry of singular sets

Source abstract

Singularity theory is concerned with the study of smooth mappings between smooth manifolds. Given two such manifolds X and Y and a pair of smooth mappings f 1 , f 2 : X → Y we say that f 1 and f 2 are -equivalent if there are diffeomorphisms α: X → X and β: Y → Y with βo f 1 oα = f 2 . Clearly -equivalence is an equivalence relation, and one aims to classify smooth mappings f: X → Y up to this equivalence.