6 research outputs found
Vanishing topology of codimension 1 multi-germs over and
We construct all 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 = or , 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)
Liftable vector fields over corank one multigerms
In this paper, a systematic method is given to construct all liftable vector
fields over an analytic multigerm of
corank at most one admitting a one-parameter stable unfolding.Comment: 34 pages. In ver. 2, several careless mistakes for calculations in
Section 6 were correcte
M-deformations of A-simple germs from R(n) to R(n+1)
All A-simple corank-1 germs from R(n) to R(n+1), where n not equal 4, have an M-deformation, that is a deformation in which the maximal numbers of isolated stable singular points are simultaneously present in the image