On the second lower quotient of the fundamental group
Algebraic Geometry
2013-06-21 v3
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.
Keywords
Cite
@article{arxiv.1304.5588,
title = {On the second lower quotient of the fundamental group},
author = {Arnaud Beauville},
journal= {arXiv preprint arXiv:1304.5588},
year = {2013}
}
Comments
The result is extended to all reasonable topological spaces