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manuscripta mathematica

, Volume 104, Issue 1, pp 97–110 | Cite as

A primary obstruction to topological embeddings¶and its applications

  • Carlos Biasi
  • Janey Daccach
  • Osamu Saeki

Abstract:

For a proper continuous map f:MN between topological manifolds M and N with m≡ dimM < dimNm+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.

Mathematics Subject Classification (2000): 57N35, 57R35, 57R42, 555N05 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Carlos Biasi
    • 1
  • Janey Daccach
    • 2
  • Osamu Saeki
    • 3
  1. 1.Departamento de Matemática, ICMC-USP, Caixa Postal 668, 13560-970, São Carlos, SP, Brazil. e-mail: biasi@icmc.sc.usp.brBR
  2. 2.Departamento de Matemática, Universidade Estatudal de Maringá, Av. Colombo 5790, 87020-900, Maringá, PR, Brazil. e-mail: janey@gauss.dma.uem.brBR
  3. 3.Department of Mathematics, Graduate School of Science, Hiroshima University, Higashi-Hiroshima 739-8526, Japan. e-mail: saeki@math.sci.hiroshima-u.ac.jpJP

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