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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