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arXiv · 1112.0541

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

Mohamed Mouçouf·Youssef Alaoui
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Abstract

In this paper, we prove by means of a counterexample that there exist pair of integers (n,p) with $n\geq 3$, $2\leq p\leq n-1$, 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.

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Mohamed Mouçouf, Youssef Alaoui. 2011-12-02. On the integral homology and counterexamples to the Andreotti-Grauert conjecture. https://arxiv.org/abs/1112.0541

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