Commentarii Mathematici Helvetici

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Volume 78, Issue 3, 2003, pp. 627–647

DOI: 10.1007/s00014-003-0758-9

Fold maps on 4-manifolds

OSAMU SAEKI (1)

(1) FACULTY OF MATHEMATICS, KYUSHU UNIVERSITY, HAKOZAKI, 812-8581, FUKUOKA, JAPAN

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.

Keywords: Fold map, 4-manifold, embedded surface, characteristic class, homotopy principle, vector field, stable span