I am reading "Morse theory" by Milnor and on page 27 we have proved that the homotopy type of CP^n is of a CW-complex of the form : a 0-cell attached to a 2-cell attached to a 4-cell ... attached to a 2n-cell.µ Then Milnor says it follows that the integral homology groups of CP^n are given by H-i(CP^n;Z) = Z for i = 0,2,4,...,2n and H-i(CP^n;Z) = 0 for other values of i.
So here is my question : what is the link between homotopy type and homology in my precis case ?
Thanks !