Cooper, T., Mond, D. (David) and Wik Atique, R.. (2002) Vanishing topology of codimension 1 multi-germs over $\Bbb R$ and $\Bbb C$. Compositio Mathematica, Vol.13 (No.2). pp. 121-160. ISSN 0010-437X

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Abstract

We construct all $\cal A$e-codimension 1 multi-germs of analytic (or smooth) maps (kn, T) [rightward arrow] (kp, 0), with n [gt-or-equal, slanted] 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 [less-than-or-eq, slant] 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 [gt-or-equal, slanted] p).

Item Type:	Journal Article
Subjects:	Q Science > QA Mathematics
Divisions:	Faculty of Science > Mathematics
Library of Congress Subject Headings (LCSH):	Perturbation (Mathematics), Topology, Discriminant analysis, Singularities (Mathematics), Deformations of singularities
Journal or Publication Title:	Compositio Mathematica
Publisher:	Cambridge University Press
ISSN:	0010-437X
Date:	April 2002
Volume:	Vol.13
Number:	No.2
Page Range:	pp. 121-160
Identification Number:	10.1023/A:1014930205374
Status:	Peer Reviewed
Access rights to Published version:	Open Access
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URI:	http://wrap.warwick.ac.uk/id/eprint/792

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