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Chapitre D'ouvrage Année : 2014

On the second lower quotient of the fundamental group

Résumé

Let X be a reasonable topological space, G its fundamental group, 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) = Z/2 (due to Collino) when X is the Fano surface parametrizing lines in a cubic threefold.

Dates et versions

hal-00872559 , version 1 (14-10-2013)

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Arnaud Beauville. On the second lower quotient of the fundamental group. Algebraic and Complex Geometry, 71, Springer, pp.41-45, 2014, Proceedings in Math. & Stat. ⟨hal-00872559⟩
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