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Vanishing topology of codimension 1 multi-germs over $\Bbb R$ and $\Bbb C$
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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. doi:10.1023/A:1014930205374 ISSN 0010-437X.
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Official URL: http://dx.doi.org/10.1023/A:1014930205374
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 | ||||
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Subjects: | Q Science > QA Mathematics | ||||
Divisions: | Faculty of Science, Engineering and Medicine > 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 | ||||
Official Date: | April 2002 | ||||
Dates: |
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Volume: | Vol.13 | ||||
Number: | No.2 | ||||
Page Range: | pp. 121-160 | ||||
DOI: | 10.1023/A:1014930205374 | ||||
Status: | Peer Reviewed | ||||
Access rights to Published version: | Open Access (Creative Commons) |
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