The topological period-index conjecture (Q2166370)

The paper is devoted to proving a theorem solving the so-called topological period-index conjecture under some conditions: the index \(\mathrm{ind}(\alpha)\) in the Brauer group \(\mathrm{Br}(X)= \mathrm{H}^3(X;\mathbb Z)_{\mathrm{tor}}\) of a \(2d\)-dimensional CW-complex \(X\) is a divisor of \[ n^{d-1}\prod_{\substack{p|n,\\ (p,n) =1}} p^{\mathrm{val}_p((d-1)!) }, \] where \(n= \mathrm{per}(\alpha)\) is the period of \(\alpha\).