Abstract
AbstractLetf:M→Nbe a smooth map of a closedn-manifold into ap-manifold (n≥p) having only Morin singularities [17]. We study the topology of such a map and obtain a modulo 2 congruence formula involving the Euler characteristics ofM, N, the singular sets and the regular fibres off. We also consider applications of this formula to the existence problem of maps having only fold singular points. Stable maps into 3-manifolds are also studied and we obtain a modulo 2 congruence formula involving the swallow tails and the number of triple points of the discriminant set.
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