which the double plumbing ${N_{m,n}}$ arises as a submanifold in a closed 4–manifold $X$. In Subsection \[CP\] we consider the case $X={\mathbb {C}}P^{2}\# {\mathbb {C}}P^{2}$ and in Subsection \[S2\] the case $X=S^{2}\times S^{2}\# S^{2}\times S^{2}$. In Section \[One\] we investigate single plumbings of two disk bundles over spheres. We consider such configurations inside the manifold ${\mathbb {C}}P^{2}\# {\mathbb {C}}P^{2}$ in Subsection \[CP1\] and inside the manifold $S^{2}\times S^{2}\# S^{2}\times S^{2}$ in Subsection \[S21\].

[**Acknowledgments:**]{} I would like to thank my advisor Sašo Strle for all his help and support during our numerous discussions. I am also very grateful to the referees for a careful reading, many helpful comments and suggestions.

[Heegaard–Floer homology of the boundary of a double plumbing]{} Let $N_{m,n}$ be the double plumbing of two disk bundles over spheres, where $m$ and $n$ denote the Euler numbers of the disk bundles contained in the plumbing. The base spheres of the bundles intersect twice inside the plumbing and we assume both intersections carry the same sign. Denote by $Y_{m,n}$ the boundary of $N_{m,n}$. Throughout this paper we assume $m,n\geq 4$. In this section we calculate $HF^{+}(Y_{m,n})$ with ${\mathbb{F}}$ coefficients and prove Theorem \[th1\].

[Heegaard diagram]{} \[HD\] Considering a Kirby 