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

TL;DR

This paper completes the analysis of the topological period-index problem for 8-dimensional CW complexes, establishing the maximum index of certain Brauer classes with period divisible by 4.

Contribution

It determines the precise upper bound of the index for topological Brauer classes on 8-dimensional CW complexes with period divisible by 4.

Findings

Established the sharp upper bound of the index for relevant Brauer classes.

Extended previous work to fully resolve the period-index problem in this dimension.

Provided a complete classification of the index in the specified setting.

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.