庞加莱对偶复形的局部惰性
Local Inertness of Poincaré duality complexes
AI总结：
该研究证明特定同调条件下庞加莱对偶复形顶胞附着映射局部化后惰性，改进了已有结果，还给出6维庞加莱对偶复形的环空间分解，并得到非惰性p-局部映射的新例子。
AI中文摘要：
我们证明，在特定同调条件下，当从有限素数集合中局部化后，庞加莱对偶复形的顶胞附着映射是惰性的。在这些情况下，这改进了Félix和Tanré的结果。作为该方法的另一个应用，我们给出了满足特定假设的单连通6维庞加莱对偶复形的环空间分解。我们还证明，在惰性定理的假设下，n维庞加莱对偶复形的(n-1)维骨架在从一个明确的有限素数集合中局部化后满足双曲形式的Moore猜想，并利用这一点得到了球之间非惰性的p-局部映射的新例子。
英文摘要：
We prove that, under certain homological conditions, the attaching map of the top cell of a Poincaré duality complex is inert when localised away from a finite set of primes. This improves on a result of Félix and Tanré in these cases. As an additional application of the methods, we give a loop space decomposition of simply-connected $6$-dimensional Poincaré duality complexes satisfying certain hypotheses. We also show that, under the hypotheses of the inertness theorem, the $(n-1)$-skeleton of an $n$-dimensional Poincaré 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.
