One has two notions of vanishing cycles: the Deligne's general notion and a concrete one used recently in the study of polynomial functions. We compare these two notions which gives us in particular a relative connectivity result. We finish with an example of vanishing cycle calculation which shows the difficulty of a good choice of compactification.
@article{urn:eudml:doc:44495,
title = {Topologie des fonctions r\'eguli\`eres et cycles \'evanescents.},
journal = {Revista Matem\'atica de la Universidad Complutense de Madrid},
volume = {16},
year = {2003},
pages = {131-149},
zbl = {1073.14512},
mrnumber = {MR2031879},
language = {fr},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:44495}
}
Brélivet, Thomas. Topologie des fonctions régulières et cycles évanescents.. Revista Matemática de la Universidad Complutense de Madrid, Tome 16 (2003) pp. 131-149. http://gdmltest.u-ga.fr/item/urn:eudml:doc:44495/