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On the Betti number of the image of a codimension-$ k$ immersion with normal crossings

Authors: Carlos Biasi and Osamu Saeki
Journal: Proc. Amer. Math. Soc. 123 (1995), 3549-3554
MSC: Primary 57R42; Secondary 57R40
MathSciNet review: 1273476
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Abstract: Let $ f:M \to N$ be a codimension-k immersion with normal crossings of a closed m-dimensional manifold. We show that f is an embedding if and only if the $ (m - k + 1)$-th Betti numbers of M and $ f(M)$ coincide, under a certain condition on the normal bundle of f.

References [Enhancements On Off] (What's this?)

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