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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

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.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1995-1273476-6
PII: S 0002-9939(1995)1273476-6
Article copyright: © Copyright 1995 American Mathematical Society