## Abstract

For a proper continuous map f : M →• N between topological manifolds M and N with m = dim M < dim N = m + k, a primary obstruction to topological embeddings θ(f) ∈ H^{c}_{m-k}(M; Z_{2}) has been defined and studied by the authors in [9,8.2,3], where H^{c}_{*} denotes the singular homology with closed support. In this paper, we study the obstruction from the viewpoint of differential topology and give various applications. We first give some characterizations of embeddings among generic differentiable maps, which are refinements of the results in [9,10]. Then we give a result concerning the number of connected components of the complement of the image of a codimension-1 continuous map with a normal crossing point, which generalizes the results in [6,4,5,9]. Finally we give a simple proof of a theorem of Li and Peterson [20] about immersions of m-manifolds into (2m - 1 )-manifolds.

Original language | English |
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Pages (from-to) | 97-110 |

Number of pages | 14 |

Journal | Manuscripta Mathematica |

Volume | 104 |

Issue number | 1 |

DOIs | |

Publication status | Published - Jan 2001 |

Externally published | Yes |

## All Science Journal Classification (ASJC) codes

- General Mathematics