It is clear that the symmetric group on n + 1 letters acts on the nth singular chain group by permuting the arguments of a simplex. Suppose we divide out that action by identifying p(sigma) with sgn(p).sigma for each permutation p. This gives a quotient of the singular chain complex. Is it known if it is equivalent to it? The standard argument in the simplicial case seems to break down because two simplexes can have the same vertices without being the same. Michael Barr