Embeddings of nonorientable 4-manifolds in \(R^ 6\) (Q1922748)

This paper conjectures that a nonorientable closed smooth (topological) 4-manifold \(M\) imbeds smoothly (locally flat) in \(\mathbb{R}^6\) if and only if \(\overline{W}_2(M)=0\) (and the Kirby-Siebenmann invariant is zero). For an oriented 4-manifold imbedding in \(\mathbb{R}^6\) has been understood for some time. The author is attempting to extend the result to the nonorientable case and obtains several imbedding results supporting this conjecture.