Subject: I stand corrected Date: Wed, 07 Nov 2001 11:00:57 -0500 From: jim stasheff To: dondavis I stand corrected Dear Jim, What the messages you forwarded to me last week correspond to ? The references do not seem to be complete. In any case it is wrong to write that N-complexes are equivalent to complexes. This is only true in some sense for the simplicial case combined with (generalized) N-roots of unity and as far as I know the most general results of this kind are the ones contained in my paper of 1998 in K-theory. However generically a N-complex does not rely on a complex and there are properties of the homology of N-complexes N \geq 3 with no analog in the case N=2, (i.e. for ordinary complexes), such e.g. the exact hexagons connecting the components of the homology of a N-complex. The examples connected with physics that I have studied with Marc (for higher spin gauge fields) and with Ivan Todorov (for WZNW-models) cannot be reduced to complexes, (I gave a relatively complete summary of these topics in my lectures in Bariloche (math.QA/0005256). Amities Michel Dubois-Violette