let S be the n-sphere. how can we see that
(SxS) smash S
has the homotopy type of a wedge of spheres?
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2$\begingroup$ Is this homework? $\endgroup$– Fernando MuroMar 29, 2011 at 15:48
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1 Answer
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More generally the suspension $S\land(X\times Y)$ of $X\times Y$ is the wedge of the suspensions of $X$, $Y$, and the smash product $X\land Y$; see for example proposition 4.74 of Hatcher's book.
answered Mar 29, 2011 at 17:08