Cohomology of configuration space of a compact manifold - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-25T16:38:27Z http://mathoverflow.net/feeds/question/122740 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/122740/cohomology-of-configuration-space-of-a-compact-manifold Cohomology of configuration space of a compact manifold Hicham YAMOUL 2013-02-23T18:09:36Z 2013-02-24T08:06:55Z <p>There is a reference or a methode which by it we can calculate the cohomology of a configuration space of a compact manifold simply connected? It is possible to find a spectral sequence converging to this cohomology (but the Cohen-Taylor spectral sequence)?</p> http://mathoverflow.net/questions/122740/cohomology-of-configuration-space-of-a-compact-manifold/122789#122789 Answer by Dan Petersen for Cohomology of configuration space of a compact manifold Dan Petersen 2013-02-24T08:06:55Z 2013-02-24T08:06:55Z <p>I would be extremely surprised if there was anything other than the Cohen-Taylor spectral sequence that you can do in this generality.</p> <p>As you know, the first nontrivial page of Cohen-Taylor spectral sequence depends only on the ring \$H^\bullet(M)\$. I think it's written up somewhere that the higher order differentials are defined by Massey products on \$M\$. In particular the result you refer to in a comment that \$H^\bullet(F(M,n))\$ (or its associated graded) can be computed explicitly from \$H^\bullet(M)\$ extends to arbitrary formal manifolds \$M\$, not just smooth projective varieties. And if you give yourself a minimal model of \$M\$ you should be able to compute \$H^\bullet(F(M,n))\$ for all \$n\$ as well (but not a minimal model of \$F(M,n)\$ -- see the paper of Longoni and Salvatore).</p>