Subject: For AlgTop list. Date: Tue, 30 Oct 2001 18:33:46 +0000 From: Frank Neumann To: dmd1@lehigh.edu Re: Jianzhong Pan's question on n-fold chain complexes >The question is that what is the relation between >n-chain complex and chain complex. >It seems to me that someone proved that they are equivalent in some >sense. I forget where I found this and evenworse I am not sure if it's a wrong >memory. The "someone" was Spanier. Here is the reference and the Math Review by Steenrod: Spanier, E. H. The Mayer homology theory. Bull. AMS 55, (1949). 102--112 "W. Mayer defined homology groups [Ann. of Math. (2) 43, 370--380, 594--605 (1942); these Rev. 3, 318] based on a boundary operator $\partial$ such that $\partial\sp p=0$ ($p$ a prime) instead of the usual $\partial\sp 2=0$. He obtained a doubly indexed system of groups $H\sb {n,q} (0