Resumen de The cohomology algebra of unordered configuration spaces
Given an -dimensional compact closed oriented 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, an explicit description is provided of the invariants algebra of the first term of . This determination is applied in two directions.
(a) In the case of a complex projective manifold or of an odd-dimensional manifold , the cohomology algebra of the space of unordered configurations of points in is obtained (the concrete example of is detailed).
(b) The degeneration of the spectral sequence formed of the -invariants at level 2 is proved for any manifold .
These results use a transfer map and are also true with coefficients in a finite field with .
