Geodesic
Generalised Kummer construction and the cohomology rings of $G_2$-manifolds
Sbornik. Mathematics, Tome 209 (2018) no. 12, pp. 1803-1811

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Intersection theory is used to calculate the cohomology rings of $G_2$-manifolds arising from the generalised Kummer construction. For one example, generators of the rational cohomology ring are found and their multiplication table is described. Bibliography: 19 titles.
Keywords: cohomology ring, intersection ring, manifolds with $G_2$-holonomy. 
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     title = {Generalised {Kummer} construction and the cohomology rings of $G_2$-manifolds},
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I. A. Taimanov. Generalised Kummer construction and the cohomology rings of $G_2$-manifolds. Sbornik. Mathematics, Tome 209 (2018) no. 12, pp. 1803-1811. http://geodesic.mathdoc.fr/item/SM_2018_209_12_a6/