Geodesic
The integral cohomology algebras of ordered configuration spaces of spheres
Documenta mathematica, Tome 5 (2000), pp. 115-139.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: We compute the cohomology algebras of spaces of ordered point configurations on spheres, $F(S^k,n)$, with integer coefficients. For $k=2$ we describe a product structure that splits $F(S^2,n)$ into well-studied spaces. For $k>2$ we analyze the spectral sequence associated to a classical fiber map on the configuration space. In both cases we obtain a complete and explicit description of the integer cohomology algebra of $F(S^k,n)$ in terms of generators, relations and linear bases. There is 2-torsion occuring if and only if $k$ is even. We explain this phenomenon by relating it to the Euler classes of spheres. Our rather classical methods uncover combinatorial structures at the core of the problem.
Classification : 55M99, 57N65, 55R20, 52C35
Keywords: spheres, ordered configuration spaces, subspace arrangements, integral cohomology algebra, fibration, Serre spectral sequence 
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     title = {The integral cohomology algebras of ordered configuration spaces of spheres},
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     year = {2000},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DOCMA_2000__5__a16/}
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Feichtner, Eva Maria; Ziegler, Günter M. The integral cohomology algebras of ordered configuration spaces of spheres. Documenta mathematica, Tome 5 (2000), pp. 115-139. http://geodesic.mathdoc.fr/item/DOCMA_2000__5__a16/