On mappings into ℝ2ℓ

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]. Supported by FAPESP and FINEP.