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1 results

  • Vanishing Topology of Codimension 1 Multi-germs over $\Bbb R$ and $\Bbb C$

  • T. Cooper, D. Mond, R. Wik Atique
  • Journal:
    Compositio Mathematica / Volume 131 / Issue 2 / April 2002
    Published online by Cambridge University Press:
    04 December 2007, pp. 121-160
    Print publication:
    April 2002
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  • We construct all $\cal A$e-codimension 1 multi-germs of analytic (or smooth) maps (kn, T) → (kp, 0), with n [ges ] p − 1, (n, p) nice dimensions, k = $\mathbb C$ or $\mathbb R$, by augmentation and concatenation operations, starting from mono-germs (|T| = 1) and one 0-dimensional bi-germ. As an application, we prove general statements for multi-germs of corank [les ] 1: every one has a real form with real perturbation carrying the vanishing homology of the complexification, every one is quasihomogeneous, and when n = p − 1 every one has image Milnor number equal to 1 (this last is already known when n [ges ] p).