Abstract
LetM be a compact orientable manifold. We know how to calculateX(M), the Euler characteristic ofM, from a stable mapf: M→R, with information only onS(f), the singular set off. This result was extended to stable maps into the plane by H. Levine [L-2] whenM has dimension 2n, and it is also calculated fromS(f). The purpose of this work is to generalize the above result for maps intoR 2l, wheren≥l. In this caseS(f) is not a manifold. We use the process of resolution of singularities [L-3] to get a homomorphism having only singularities of codimension 1 and use simmilar technics as in [L-2].
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References
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Kushner, L. On mappings into ℝ2ℓ . Bol. Soc. Bras. Mat 13, 45–54 (1982). https://doi.org/10.1007/BF02584734
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DOI: https://doi.org/10.1007/BF02584734