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On the second lower quotient of the fundamental group

Abstract : 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.
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Contributor : Arnaud Beauville <>
Submitted on : Monday, October 14, 2013 - 7:45:17 AM
Last modification on : Monday, October 12, 2020 - 10:27:31 AM

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  • HAL Id : hal-00872559, version 1
  • ARXIV : 1304.5588



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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