  Let PConf^n M be the configuration space of ordered n-tuples of distinct
points on a smooth manifold M admitting a nowhere-vanishing vector field. We
show that the ith cohomology group with coefficients in a field H^i(PConf^n M,
k) is an N-module, where N is the category of noncommutative finite sets
introduced by Pirashvili and Richter. Studying the representation theory of N,
we obtain new polynomiality results for the cohomology groups H^i(PConf^n M,
k). In the case of unordered configuration space Conf^n M = (PConf^n M)/S_n and
rational coefficients, we show that cohomology dimension in fixed degree is
nondecreasing.
