Answer by Eric Wofsey for Concerning homotopy groups of a finite wedge of...
No, $\pi_n(X)$ is not even a free $\mathbb{Z}$-module for most values of $n$. Indeed, if $m>1$, then $\pi_n(S^m)$ has torsion for infinitely many values of $n$. Since each of the spheres in $X$ is a...
View ArticleConcerning homotopy groups of a finite wedge of spheres
Let $X$ be a finite wedge of $m$-spheres containing some circles. Is $\pi_n (X)$ a free $\mathbb{Z}\pi_1 (X)$-module, for all $n\geq 2$?
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