For any manifold $M$, the unordered configuration space of $k$ points is obtaibned obtained as a quotient of ordered configuration space of $k$ points by the group action of symmetric group on $k$ letters. Does it induce some relation between the cohomology algebras of the two spaces?
For any manifold $M$, the unordered configuration space of $k$ points is obtaibned as a quotient of ordered configuration space of $k$ points by the group action of symmetric group on $k$ letters. Does it induce some relation between the cohomology algebras of the two spaces?