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arXiv · 2106.08055

Loop space decompositions of $(2n-2)$-connected $(4n-1)$-dimensional Poincar\'{e} Duality complexes

Ruizhi Huang·Stephen Theriault
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Abstract

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.

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Ruizhi Huang, Stephen Theriault. 2021-06-15. Loop space decompositions of $(2n-2)$-connected $(4n-1)$-dimensional Poincar\'{e} Duality complexes. https://doi.org/10.1007/s40687-022-00338-y

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