A note on separation properties of codimension-1 immersions with normal crossings

Carlos Biasi, Walter Motta, Osamu Saeki

Research output: Contribution to journalArticle

8 Citations (Scopus)

Abstract

Let f: Mn-1 → Nn be an immersion with normal crossings between closed connected manifolds. The article is concerned with the problem of separation of N by f(M). The main result of this paper is a converse of the Jordan-Brouwer Theorem, under the hypothesis that M is oriented and H1(N;Z2) = 0. More precisely, with the above hypothesis, f is an embedding if and only if N - f(M) has two connected components.

Original languageEnglish
Pages (from-to)81-87
Number of pages7
JournalTopology and its Applications
Volume52
Issue number1
DOIs
Publication statusPublished - Aug 13 1993
Externally publishedYes

Fingerprint

Separation Property
Immersion
Codimension
Brouwer's theorem
Connected Components
Converse
If and only if
Closed

All Science Journal Classification (ASJC) codes

  • Geometry and Topology

Cite this

A note on separation properties of codimension-1 immersions with normal crossings. / Biasi, Carlos; Motta, Walter; Saeki, Osamu.

In: Topology and its Applications, Vol. 52, No. 1, 13.08.1993, p. 81-87.

Research output: Contribution to journalArticle

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