Originally Posted by

**jonathan122** Hi,

Given a space X, it can be shown (either via the Mayer-Vietoris theorem, or by theory of exact sequences and relative homology) that, for all n, we have H~_n(X)=H~_n+1(SX), where SX is the suspension of X, and I'm using H~ to stand for the reduced homology.

I'm trying to find an explicit chain map from C_n(X) to C_n+1(SX) which induces this isomorphism, but I'm not really sure where to start. Does anyone have any ideas? (This is question 21 in Hatcher, Section 2.1, if that helps at all.)

Thanks,

Jonathan.