Abstract
Let X be a topological space, G = π 1(X) and D = (G, G). We express the second quotient D∕(D, G) of the lower central series of G in terms of the homology and cohomology of X. As an example, we recover the isomorphism \(D/(D,G)\mathop{\cong}\mathbb{Z}/2\) (due to Collino) when X is the Fano surface parametrizing lines in a cubic threefold.
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References
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Dedicated to Klaus Hulek on his 60th birthday
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Beauville, A. (2014). On the Second Lower Quotient of the Fundamental Group. In: Frühbis-Krüger, A., Kloosterman, R., Schütt, M. (eds) Algebraic and Complex Geometry. Springer Proceedings in Mathematics & Statistics, vol 71. Springer, Cham. https://doi.org/10.1007/978-3-319-05404-9_2
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DOI: https://doi.org/10.1007/978-3-319-05404-9_2
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