Subject: chain complex with trivial composition of n boundary operators Date: Mon, 29 Oct 2001 16:50:14 +0800 From: "pjz" To: First, thanks to all those who answer kindly my question about the relation between vector bundle and algebraic vector bundle. The information is useful to me. Actually I was able to prove the following in a not so precise statement: Algebraic K-theory isomorphism implies topological K-theory isomorphism and possibly semi-K-thoery isomorphism . More precise results will appear shortly. Does any one know similar kind of results? Second , a question about chain complex. Let us call temporarily a complex of free abelian groups with boundary operators $d_i$ a n-chain complex if $d_m \circ \cdots \circ d_{m+n}=0$ for each m. Of course a 2-chain complex is an ordinary chain complex . 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. Best wishes Jianzhong Pan