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Studying the topology of Morin singularities from a global viewpoint

Published online by Cambridge University Press:  24 October 2008

Osamu Saeki
Osamu Saeki
Affiliation:
Department of Mathematics, Faculty of Science, Hiroshima University, Higashi-Hiroshima 724, Japan
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Abstract

Let f: M → N be a smooth map of a closed n-manifold into a p-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 of M, N, the singular sets and the regular fibres of f. 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.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 117 , Issue 2 , March 1995 , pp. 223 - 235
Copyright
Copyright © Cambridge Philosophical Society 1995

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