Author:
Breva Ribes I.,Oset Sinha R.
Abstract
AbstractWe study the simplicity of map-germs obtained by the operation of augmentation and describe how to obtain their versal unfoldings. When the augmentation comes from an $${\mathscr {A}}_e$$
A
e
-codimension 1 germ or the augmenting function is a Morse function, we give a complete characterisation for simplicity. These characterisations yield all the simple augmentations in all explicitly obtained classifications of $${\mathscr {A}}$$
A
-simple monogerms except for one ($$F_4$$
F
4
in Mond’s list from $$\mathbb C^2$$
C
2
to $$\mathbb C^3$$
C
3
). Moreover, using our results we produce a list of corank 1 simple augmentations from $$\mathbb C^4$$
C
4
to $$\mathbb C^4$$
C
4
.
Funder
Ministerio de Ciencia, Innovación y Universidades
Publisher
Springer Science and Business Media LLC
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