On the integral homology and counterexamples to the Andreotti-Grauert conjecture

In this paper, we prove by means of a counterexample that there exist pair of integers (n,p) with $n\ge 3$, $2\le p\le n-1$, and open sets $D$ in $C^n$ which are cohomologically $p$-complete with respect to the structure sheaf of $D$ such that the cohomology group $H_{n+p}(D,Z)$ does not vanish. In particular $D$ is not $p$-complete.