EXISTENCE OF FOLD MAPS OF 6-DIMENSIONAL MANIFOLDS INTO ℝ⁵

Abstract

We give some sufficient and necessary conditions for the existence of fold maps of orientable 6-dimensional manifolds into ℝ⁵ with a prescribed singular set. To get the results, we study the relative half Euler characteristic of linearly independent vector fields. As a corollary we obtain that there are fold maps of S⁶ into ℝ⁵ whose singular sets consist of aspherical homology 4-spheres.