A free (Z/2)^r action on a product of real projective spaces, with trivial action on mod-2 cohomology, forces r ≤ mu(n_1)+...+mu(n_k), proving a homotopy-theoretic form of Cusick's conjecture.
Carlsson,On the rank of abelian groups acting freely on(S n)k, Invent
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Free actions on products of real projective spaces
A free (Z/2)^r action on a product of real projective spaces, with trivial action on mod-2 cohomology, forces r ≤ mu(n_1)+...+mu(n_k), proving a homotopy-theoretic form of Cusick's conjecture.