## 抄録

We give two congruence formulas concerning the number of non-trivial double point circles and arcs of a smooth map with generic singularities - the Whitney umbrellas - of an n-manifold into R^{2n-1}, which generalize the formulas by Sziics for an immersion with normal crossings. Then they are applied to give a new geometric proof of the congruence formula due to Mahowald and Lannes concerning the normal Euler number of an immersed n-manifold in R^{2n}. We also study generic projections of an embedded nmanifold in R^{2n} into R^{2n-1} and prove an elimination theorem of Whitney umbrella points of opposite signs, which is a direct generalization of a recent result of Carter and Saito concerning embedded surfaces in R^{4}. The problem of lifting a map into R^{2n-1} to an embedding into R^{2n} is also studied.

本文言語 | 英語 |
---|---|

ページ（範囲） | 2585-2606 |

ページ数 | 22 |

ジャーナル | Transactions of the American Mathematical Society |

巻 | 348 |

号 | 7 |

出版ステータス | 出版済み - 1996 |

外部発表 | はい |

## !!!All Science Journal Classification (ASJC) codes

- 数学 (全般)
- 応用数学

## フィンガープリント

「Immersed n-manifolds in R^{2n}and the double points of their generic projections into R

^{2n-1}」の研究トピックを掘り下げます。これらがまとまってユニークなフィンガープリントを構成します。