On pairs of locally flat 2-spheres in simply connected 4-manifolds (Q1127657)

A necessary and sufficient condition for the representation of a pair of mutually orthogonal primitive classes by disjoint locally flat spheres with nice complement is proven. The necessity of the condition is proven following \textit{V. A. Rokhlin} [Funct. Anal. Appl. 5, 39-48 (1971); translation from Funkts. Anal. Prilozh. 5, No. 1, 48-60 (1971; Zbl 0268.57019)] and the sufficiency following the basic outline and extending ideas of \textit{I. Hambleton} and \textit{M. Kreck} [J. Reine Angew. Math. 443, 21-47 (1993; Zbl 0779.57014)] and of \textit{R. Lee} and \textit{D. M. Wilczyński} [Comment. Math. Helv. 65, No. 3, 388-412 (1990; Zbl 0723.57015); K-Theory 7, No. 4, 333-367 (1993; Zbl 0805.57014)]. The condition is an inequality which depends on homological data.