Loop space decompositions of $(2n-2)$-connected $(4n-1)$-dimensional Poincaré Duality complexes

Abstract

Beben and Wu showed that if $M$ is a $(2n-2)$-connected $(4n-1)$-dimensional Poincaré Duality complex such that $n\ge 3$ 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.

26 pages; slightly modified

Cited by in corpus (2)

• Suspension homotopy of $6$-manifolds
• Loop homotopy of $6$-manifolds over $4$-manifolds