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arXiv · 2502.15385

Loop spaces of $n$-dimensional Poincar\'e duality complexes whose $(n-1)$-skeleton is a co-$H$-space

Lewis Stanton·Stephen Theriault
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Abstract

Under certain hypotheses, we prove a loop space decomposition for simply-connected Poincar\'e Duality complexes of dimension $n$ whose $(n-1)$-skeleton is a co-$H$-space. This unifies many known decompositions obtained in different contexts and establishes many new families of examples. As consequences, we show that such a looped Poincar\'{e} Duality complex retracts off the loops of its $(n-1)$-skeleton and describe its homology as a one-relator algebra.

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Lewis Stanton, Stephen Theriault. 2025-02-21. Loop spaces of $n$-dimensional Poincar\'e duality complexes whose $(n-1)$-skeleton is a co-$H$-space. https://arxiv.org/abs/2502.15385

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