A note on free actions of groups on products of spheres

J. H. Jo, J. B. Lee


It has been conjectured that if $G = (\bbz_{p})^r$ acts freely on a finite $CW$-complex $X$ which is homotopy equivalent to a product of spheres $S^{n_1} \times
S^{n_2} \times \cdots \times S^{n_k}$, then $r \leq k$.
We ask the question with the relaxation that $X$ is finite-dimensional,
and show that it suffices to consider the case
that the dimension of spheres are greater than or equal to $2$ in order to answer the question.



CW-complex, free action, free rank, solvmanifolds, strongly polycyclic groups

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Bulletin of the Aust. Math. Soc., copyright Australian Mathematical Publishing Association Inc.