### 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 language | English |
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Pages (from-to) | 223-235 |

Number of pages | 13 |

Journal | Mathematical Proceedings of the Cambridge Philosophical Society |

Volume | 117 |

Issue number | 2 |

DOIs | |

Publication status | Published - Jan 1 1995 |

Externally published | Yes |

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### All Science Journal Classification (ASJC) codes

- Mathematics(all)

### Cite this

**Studying the Topology of Morin Singularities from a Global Viewpoint.** / Saeki, Osamu.

Research output: Contribution to journal › Article

}

TY - JOUR

T1 - Studying the Topology of Morin Singularities from a Global Viewpoint

AU - Saeki, Osamu

PY - 1995/1/1

Y1 - 1995/1/1

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.

UR - http://www.scopus.com/inward/record.url?scp=84973954051&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84973954051&partnerID=8YFLogxK

U2 - 10.1017/S0305004100073072

DO - 10.1017/S0305004100073072

M3 - Article

VL - 117

SP - 223

EP - 235

JO - Mathematical Proceedings of the Cambridge Philosophical Society

JF - Mathematical Proceedings of the Cambridge Philosophical Society

SN - 0305-0041

IS - 2

ER -