The topological period–index problem over 8‐complexes, I

Abstract

We study the Postnikov tower of the classifying space of a compact Lie group P ( n , m n ) , which gives obstructions to lifting a topological Brauer class of period n to a P U m n -torsor, where the base space is a CW complex of dimension 8 . Combined with the study of a twisted version of Atiyah–Hirzebruch spectral sequence, this solves the topological period–index problem for CW complexes of dimension 8.