TY - JOUR
T1 - A note on separation properties of codimension-1 immersions with normal crossings
AU - Biasi, Carlos
AU - Motta, Walter
AU - Saeki, Osamu
N1 - Funding Information:
668, 13560-250 SLo Carlos, Brazil. * Partially supported by CNPq.
PY - 1993/8/13
Y1 - 1993/8/13
N2 - 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.
AB - 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.
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U2 - 10.1016/0166-8641(93)90093-S
DO - 10.1016/0166-8641(93)90093-S
M3 - Article
AN - SCOPUS:38249000137
VL - 52
SP - 81
EP - 87
JO - Topology and its Applications
JF - Topology and its Applications
SN - 0166-8641
IS - 1
ER -