The nth configuration space. Conf_n(X), of a topological space X, is the space of n distinct points in X. In formulas, Conf_n(X) := {(X_1, ...,x_n) x_i ≠ x_j if i≠j}. This is often called the ordered configuration space. There is a natural action of the symmetric group S_n on Conf_n(X) which reorders the indices of the n-tuple; the quotient Conf_n(X)/S_n by this action is therefore the unordered configuration space.
展开▼
