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Real deformations and invariants of map-germs

J. H. Rieger;  M. A. S. Ruas;  R. Wik Atique — 2008

Banach Center Publications

A stable deformation f t of a real map-germ f : ℝ ⁿ , 0 → ℝ p , 0 is said to be an M-deformation if all isolated stable (local and multi-local) singularities of its complexification f ℂ t are real. A related notion is that of a good real perturbation f t of f (studied e.g. by Mond and his coworkers) for which the homology of the image (for n < p) or discriminant (for n ≥ p) of f t coincides with that of f C t . The class of map germs having an M-deformation is, in some sense, much larger than the one having a good real perturbation....

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