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Multiplicity of Boardman strata and deformations of map germs

Published online by Cambridge University Press:  18 May 2009

J. J. Nuño Ballesteros  and
M. J. Saia
J. J. Nuño Ballesteros
Affiliation:
Departament de Geometria I Topologia, Universitat de ValènciaCampus de Burjassot, 46100 Burjassot, Spain email: [email protected]
M. J. Saia
Affiliation:
Instituto de Geociências E Ciencias Exatas, Universidade Estadual Paulista Campus de Rio Claro, Caixa Postal 178, 13500-230, Rio Claro, SP, Brazil email: [email protected]
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Abstract

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We define algebraically for each map germ f:Kn,0→Kp, 0 and for each Boardman symbol i=(i1,…,ik) a number ci(f) which is -invariant. If f is finitely determined, this number is the generalization of the Milnor number of f when p = 1, the number of cusps of f when n = p = 2, or the number of cross caps when n = 2, p = 3. We study some properties of this number and prove that, in some particular cases, this number can be interpreted geometrically as the number of Σi points that appear in a generic deformation of f. In the last part, we compute this number in the case that the map germ is a projection and give some applications to catastrophe map germs.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 40 , Issue 1 , March 1998 , pp. 21 - 32
Copyright
Copyright © Glasgow Mathematical Journal Trust 1998

References

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