A primary obstruction to topological embeddings and its applications

Carlos Biasi, Janey Daccach, Osamu Saeki

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)

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) ∈ 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.

Original languageEnglish
Pages (from-to)97-110
Number of pages14
JournalManuscripta Mathematica
Volume104
Issue number1
DOIs
Publication statusPublished - Jan 1 2001
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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