Two seemingly unrelated problems are intimately connected. The first is the equsingularity problem in R: For an analytic family ft : (R , 0) → (R, 0), when should it be called an “equisingular deformation”? This amounts to finding a suitable trivialization condition (as strong as possible) and, of course, a criterion. The second is on the Morse stability. We define R∗, which is R “enriched” wit...
