6-复形上的拓扑周期指数问题
The topological period-index problem over 6-complexes
摘要：
通过比较射影酉群分类空间的Postnikov塔和扭曲Atiyah-Hirzebruch谱序列中的微分，我们得到了关于周期的拓扑指数的一个下界，并完全解决了维数不超过6的有限CW复形的周期指数问题的拓扑形式.条件的建立，如果他们满足一个光滑的复杂的3倍品种的上同调，将反驳普通的周期指数猜想。满足这些条件的高维品种的例子。我们使用我们的结果来阻碍实现周期2 Brauer类作为与Clifford代数层相关的类，并构造了总Clifford不变映射不是满射的簇。以前没有这样的例子。
英文摘要：
By comparing the Postnikov towers of the classifying spaces of projective unitary groups and the differentials in a twisted Atiyah-Hirzebruch spectral sequence, we deduce a lower bound on the topological index in terms of the period, and solve the topological version of the period-index problem in full for finite CW complexes of dimension at most 6. Conditions are established that, if they were met in the cohomology of a smooth complex 3-fold variety, would disprove the ordinary period-index conjecture. Examples of higher-dimensional varieties meeting these conditions are provided. We use our results to furnish an obstruction to realizing a period-2 Brauer class as the class associated to a sheaf of Clifford algebras, and varieties are constructed for which the total Clifford invariant map is not surjective. No such examples were previously known.
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