Equisingularity in R2 As Morse Stability
Tzee-Char Kuo, Laurentiu Paunescu
Abstract
Two seemingly unrelated problems are intimately connected. The first is the equsingularity problem in 2: For an analytic family ft:(2,0) (,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 *, which is "enriched" with a class of infinitesimals. How to generalize the Morse Stability Theorem to polynomials over *?
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