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

Published online by Cambridge University Press:  04 December 2007

T. Cooper ,
D. Mond  and
R. Wik Atique
T. Cooper
Affiliation:
Mathematics Institute, University of Warwick, Coventry CV4 7AL, United Kingdom
D. Mond
Affiliation:
Mathematics Institute, University of Warwick, Coventry CV4 7AL, United Kingdom. E-mail: [email protected]
R. Wik Atique
Affiliation:
Instituto de Ciências Matemâticas e de Computação, Caixa Postal 668, Sao Carlos, SP CEP 13560-970, Brazil. E-mail: [email protected]
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Abstract

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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).

Keywords

singularitystable perturbationvanishing topologydiscriminant
Type
Research Article
Information
Compositio Mathematica , Volume 131 , Issue 2 , April 2002 , pp. 121 - 160
Copyright
© 2002 Kluwer Academic Publishers