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We complete the study of the topological period-index problem over 8dimensional 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 8dimensional finite CW complex and the period of $\alpha$ is divisible by 4.

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