Studying the Topology of Morin Singularities from a Global Viewpoint

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13 Citations (Scopus)

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.

Original languageEnglish
Pages (from-to)223-235
Number of pages13
JournalMathematical Proceedings of the Cambridge Philosophical Society
Volume117
Issue number2
DOIs
Publication statusPublished - Mar 1995
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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