### 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 1 2001 |

Externally published | Yes |

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### All Science Journal Classification (ASJC) codes

- Mathematics(all)

### Cite this

*Manuscripta Mathematica*,

*104*(1), 97-110. https://doi.org/10.1007/s002290170048

**A primary obstruction to topological embeddings and its applications.** / Biasi, Carlos; Daccach, Janey; Saeki, Osamu.

Research output: Contribution to journal › Article

*Manuscripta Mathematica*, vol. 104, no. 1, pp. 97-110. https://doi.org/10.1007/s002290170048

}

TY - JOUR

T1 - A primary obstruction to topological embeddings and its applications

AU - Biasi, Carlos

AU - Daccach, Janey

AU - Saeki, Osamu

PY - 2001/1/1

Y1 - 2001/1/1

N2 - 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) ∈ Hcm-k(M; Z2) has been defined and studied by the authors in [9,8.2,3], where Hc* 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.

AB - 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) ∈ Hcm-k(M; Z2) has been defined and studied by the authors in [9,8.2,3], where Hc* 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.

UR - http://www.scopus.com/inward/record.url?scp=0035529593&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0035529593&partnerID=8YFLogxK

U2 - 10.1007/s002290170048

DO - 10.1007/s002290170048

M3 - Article

AN - SCOPUS:0035529593

VL - 104

SP - 97

EP - 110

JO - Manuscripta Mathematica

JF - Manuscripta Mathematica

SN - 0025-2611

IS - 1

ER -