chapter  29
25 Pages

Products

WithMarvin J. Greenberg, John R. Harper

We have seen (7.11) that the n th homotopy group of a product of pointed spaces is canonically isomorphic to the product of the n th homotopy groups of the factors. However, the behavior of the homology modules with respect to products is more complicated. For example, H 2(S 1 × S 1) ≅ R, while H 2(S 1) × H 2(S 1) = 0.