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arXiv · 2608.17563

Local Inertness of Poincar\'{e} duality complexes

Samik Basu·Sebastian Chenery·Ruizhi Huang·Lewis Stanton·Stephen Theriault
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Abstract

We prove that, under certain homological conditions, the attaching map of the top cell of a Poincar\'{e} duality complex is inert when localised away from a finite set of primes. This improves on a result of F\'elix and Tanr\'e in these cases. As an additional application of the methods, we give a loop space decomposition of simply-connected $6$-dimensional Poincar\'{e} duality complexes satisfying certain hypotheses. We also show that, under the hypotheses of the inertness theorem, the $(n-1)$-skeleton of an $n$-dimensional Poincar\'{e} duality complex satisfies the hyperbolic form of Moore's Conjecture after localising away from an explicit finite set of primes, and use this to obtain new examples of \(p\)-local maps between spheres that are not inert.

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Samik Basu, Sebastian Chenery, Ruizhi Huang, Lewis Stanton, Stephen Theriault. 2026-08-18. Local Inertness of Poincar\'{e} duality complexes. https://arxiv.org/abs/2608.17563

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