“…Surprisingly enough, for (n, p) = (4, 3), the conclusion of the above corollary does not hold in general. In fact, if a closed oriented 4-manifold M has signature σ(M ) = ±1, ±2, then M always admits a fold map into R 3 (see [27]). Note that, in this case, k = 1 and 4k = n. Remark 4.8.…”