C^O-Sufficiency of Jets

Abstract

The notion of universal unfolding has been discussed in this book on many occasions. The question of dimensional minimality of the universal unfolding will be one of our concerns in this chapter. Recall that in the definition of the universal unfolding, the map Φ is a C^∞-mapping. Thus, according to Theorem 2.2 of Chapter 3, the universal unfolding of the germ x⁴ + y⁴ is of codimension eight. However, it seems that if the map Φ is only required to be continuous (C^O-) then the codimension of the universal unfolding of the germ x⁴ + y⁴ is seven [18]. This motivates us to discuss C^O-sufficiency in greater depth.