The Topological Period-Index Problem over 8-Complexes, II

Abstract

We complete the study of the topological period-index problem over 8 dimensional finite CW complexes started in a preceding paper. More precisely, we determine the sharp upper bound of the index of a topological Brauer class $\alpha \in H^3(X;\mathbb{Z})$, where $X$ is of the homotopy type of an 8 dimensional finite CW complex and the period of $\alpha$ is divisible by 4.

14 pages, 3 figures, a sequel to arXiv: 1709.00787, minor revisions, to appear in the Proceedings of the American Mathematical Society