TY - JOUR
T1 - Studying the Topology of Morin Singularities from a Global Viewpoint
AU - Saeki, Osamu
N1 - Funding Information:
* The author is partly supported by FAPESP and CCInt-USP.
Copyright:
Copyright 2016 Elsevier B.V., All rights reserved.
PY - 1995/3
Y1 - 1995/3
N2 - 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.
AB - 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.
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U2 - 10.1017/S0305004100073072
DO - 10.1017/S0305004100073072
M3 - Article
AN - SCOPUS:84973954051
SN - 0305-0041
VL - 117
SP - 223
EP - 235
JO - Mathematical Proceedings of the Cambridge Philosophical Society
JF - Mathematical Proceedings of the Cambridge Philosophical Society
IS - 2
ER -