For polyhedral products (CA, A)^K with finite A_i of torsion-free homology, rational hyperbolicity implies no homotopy exponent at odd primes, and Moore's conjecture holds if suspensions of A_i are wedges of spheres; criteria are given for hyperbolicity in polyhedral joins.
The homotopy type of the complement of a coordinate subspace arrangement
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Homotopy exponents of polyhedral products
For polyhedral products (CA, A)^K with finite A_i of torsion-free homology, rational hyperbolicity implies no homotopy exponent at odd primes, and Moore's conjecture holds if suspensions of A_i are wedges of spheres; criteria are given for hyperbolicity in polyhedral joins.