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

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

2011-12-02

arxiv.org/abs/1112.0541v1

Global Journal of Pure and Applied Mathematics. ISSN 0973-1768 Volume 8, Number 1 (2012), pp. 1-12

Mathematics

Complex Variables

13 pages

Scientific paper

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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