Real deformations and invariants of map-germs

• Autorzy: J. H. Rieger , M. A. S. Ruas , R. Wik Atique
• Języki publikacji: EN

Abstrakty

EN

A stable deformation $f^t$ of a real map-germ $f:ℝⁿ,0 → ℝ^p,0$ 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. We show that all singular map-germs of minimal corank (i.e. of corank max(n-p+1,1)) and $𝓐_e$-codimension 1 have an M-deformation. More generally, there is the question whether all 𝓐-simple singular map-germs of minimal corank have an M-deformation. The answer is "yes" for the following three dimension ranges (n,p): n ≥ p, p ≥ 2n and p = n + 1, n ≠ 4. We describe some new techniques for obtaining these results, which lead to simpler proofs and also to new results in the dimension range n + 2 ≤ p ≤ 2n - 1.

Kategorie tematyczne

• 58K65: Topological invariants
• 32S30: Deformations of singularities; vanishing cycles
• 58K60: Deformation of singularities

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 2008
• Tom: 82
• Numer: 1
• Strony: 183-199

Daty

wydano

2008

Twórcy

autor

J. H. Rieger

• Institut für Mathematik, Universität Halle, D-06099 Halle (Saale), Germany

autor

M. A. S. Ruas

• ICMC, Universidade de São Paulo, 13560-970 São Carlos, SP, Brazil

autor

R. Wik Atique

• ICMC, Universidade de São Paulo, 13560-970 São Carlos, SP, Brazil

Identyfikatory

DOI

10.4064/bc82-0-13