at least $4$ geometric intersections, and there exist representatives with exactly $4$ intersections.\
b) Let $t\in \mathbb{N}\backslash \{1\}$ and let $a$ be an odd positive integer. Any two spheres representing classes $(a,2,0,0),(1,0,t,1)\in H_{2}(S^{2}\times S^{2}\# S^{2}\times S^{2})$ intersect with at least $4$ geometric intersections for all $a\geq 5$.

By a similar method we study single plumbings of disk bundles over spheres inside a closed 4–manifold. An obstruction to embedding such configurations is based on the $d$–invariants of lens spaces.

\[app1\] Let $k$ be a positive integer. Any two spheres representing classes $(2k+1,2,0,0),(-k,1,2k,1)\in H_{2}(S^{2}\times S^{2}\# S^{2}\times S^{2})$ intersect with at least 3 geometric intersections for all $k>1$.

This paper is organized as follows. In Subsection \[HD\] we describe a Heegaard diagram for ${Y_{m,n}}=\partial {N_{m,n}}$. In \[CF\] we present the corresponding chain complex $\widehat{CF}({Y_{m,n}})$ along with its decomposition into equivalence classes of $\sp $ structures and calculate the homology $HF^{+}({Y_{m,n}},\mathfrak{s})$ in all torsion $\sp $ structures on ${Y_{m,n}}$. In Subsection \[absolute\] we compute the absolute gradings ${\widetilde{\operatorname{gr}}}$ of the generators of these groups which in turn determine the correction term invariants $d_{b}({Y_{m,n}},\mathfrak{s})$ for all torsion $\sp $ structures $\mathfrak{s}$ on ${Y_{m,n}}$. The first part of Section \[App\] describes the general homological setting in 