The cohomology algebra of unordered configuration spaces
Abstract
Given an -dimensional compact manifold and a field , F. Cohen and L. Taylor have constructed a spectral sequence, , converging to the cohomology of the space of ordered configurations of points in . The symmetric group acts on this spectral sequence giving a spectral sequence of differential graded commutative algebras. Here, we provide an explicit description of the invariants algebra of the first term of . We apply this determination in two directions: -- in the case of a complex projective manifold or of an odd dimensional manifold , we obtain the cohomology algebra of the space of unordered configurations of points in (the concrete example of is detailed), -- we prove the degeneration of the spectral sequence formed of the -invariants at level 2, for any manifold . These results use a transfer map and are also true with coefficients in a finite field with .
Keywords
Cite
@article{arxiv.math/0311323,
title = {The cohomology algebra of unordered configuration spaces},
author = {Yves Felix and Daniel Tanré},
journal= {arXiv preprint arXiv:math/0311323},
year = {2007}
}