In this paper we classify the singular fibres of stable maps of closed (possibly non-orientable) 4-manifolds into 3-manifolds up to the $C^{\infty}$ equivalence. Furthermore, we obtain several results on the co-existence of the singular fibres of such maps. As a consequence, we show that under certain conditions, the Euler number of the source 4-manifold has the same parity as the total number of certain singular fibres. This generalises Saeki's result in the orientable case.
Publié le : 2006-07-14
Classification:
stable map,
singular fibre,
Euler number,
two colour decomposition,
57R45,
57N13
@article{1156342035,
author = {YAMAMOTO, Takahiro},
title = {Classification of singular fibres of stable maps of 4-manifolds into 3-manifolds and its applications},
journal = {J. Math. Soc. Japan},
volume = {58},
number = {3},
year = {2006},
pages = { 721-742},
language = {en},
url = {http://dml.mathdoc.fr/item/1156342035}
}
YAMAMOTO, Takahiro. Classification of singular fibres of stable maps of 4-manifolds into 3-manifolds and its applications. J. Math. Soc. Japan, Tome 58 (2006) no. 3, pp. 721-742. http://gdmltest.u-ga.fr/item/1156342035/