Equisingularity in $R^2$ As Morse Stability
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Two seemingly unrelated problems are intimately connected.
The first is the equsingularity problem in $\R^2$: For an analytic family $f_t:(\R^2,0)\rar (\R,0)$, 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" with a class of infinitesimals. How to generalize the Morse Stability Theorem to polynomials over $\R_*$?
10 pages
10 pages