Beben and Wu showed that if $M$ is a $(2n-2)$-connected $(4n-1)$-dimensional Poincar\'{ e} Duality complex such that $n\geq 3$ and $H^{ 2n}(M;\mathbb{ Z})$ consists only of odd torsion, then $\Omega M$ can be decomposed up to homotopy as a product of simpler, well studied spaces. We use a result from \cite{ BT2} to greatly simplify and enhance Beben and Wu's work and to extend it in various directions.
Categories: math.AT math.GT