### Abstract

Let f:M^{n-1}→N^{n} be an immersion with normal crossings of a closed orientable (n-1)-manifold into an orientable n-manifold. We show, under a certain homological condition, that if f has a multiple point of multiplicity m, then the number of connected components of N-f(M) is greater than or equal to m+1, generalizing results of Biasi and Romero Fuster (Illinois J. Math.36 (1992), 500-504) and Biasi, Motta and Saeki (Topology Appl.52 (1993), 81-87). In fact, this result holds more generally for every codimension-1 continuous map with a normal crossing point of multiplicity m. We also give various geometrical applications of this theorem, among which is an application to the topology of generic space curves.

Original language | English |
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Pages (from-to) | 235-247 |

Number of pages | 13 |

Journal | Geometriae Dedicata |

Volume | 57 |

Issue number | 3 |

DOIs | |

Publication status | Published - Oct 1 1995 |

Externally published | Yes |

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### All Science Journal Classification (ASJC) codes

- Geometry and Topology