Topological triviality of families of map germs from R^2 to R^2
Journal of Singularities, Tome 6 (2012), pp. 112-123
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We show that a 1-parameter unfolding F: (R^2 x R, 0) → (R^2 x R, 0) of a finitely determined map germ f is topologically trivial if it is excellent in the sense of Gaffney and the family of the discriminant curves Δ(f_t) is topologically trivial. We also give a formula to compute the number of cusps of 1-parameter unfoldings.
@article{10_5427_jsing_2012_6i,
author = {J.A. Moya-P\'erez and J. J. Nu\~no-Ballesteros},
title = {Topological triviality of families of map germs from {R^2} to {R^2}},
journal = {Journal of Singularities},
pages = {112--123},
publisher = {mathdoc},
volume = {6},
year = {2012},
doi = {10.5427/jsing.2012.6i},
url = {http://geodesic.mathdoc.fr/articles/10.5427/jsing.2012.6i/}
}
TY - JOUR AU - J.A. Moya-Pérez AU - J. J. Nuño-Ballesteros TI - Topological triviality of families of map germs from R^2 to R^2 JO - Journal of Singularities PY - 2012 SP - 112 EP - 123 VL - 6 PB - mathdoc UR - http://geodesic.mathdoc.fr/articles/10.5427/jsing.2012.6i/ DO - 10.5427/jsing.2012.6i ID - 10_5427_jsing_2012_6i ER -
%0 Journal Article %A J.A. Moya-Pérez %A J. J. Nuño-Ballesteros %T Topological triviality of families of map germs from R^2 to R^2 %J Journal of Singularities %D 2012 %P 112-123 %V 6 %I mathdoc %U http://geodesic.mathdoc.fr/articles/10.5427/jsing.2012.6i/ %R 10.5427/jsing.2012.6i %F 10_5427_jsing_2012_6i
J.A. Moya-Pérez; J. J. Nuño-Ballesteros. Topological triviality of families of map germs from R^2 to R^2. Journal of Singularities, Tome 6 (2012), pp. 112-123. doi: 10.5427/jsing.2012.6i
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