We give a complete characterization of those closed orientable 4-manifolds which admit smooth maps into R^3 with only fold singularities. We also clarify the relationship between the existence problem of fold maps and that of linearly independent vector fields on manifolds.
Cite this article
Osamu Saeki, Fold maps on 4-manifolds. Comment. Math. Helv. 78 (2003), no. 3, pp. 627–647DOI 10.1007/S00014-003-0758-9