# 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.

## Key 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.