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?
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Relation between cohomology of ordered and unordered configuration 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?
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