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,mn), which gives obstructions to lifting a topological Brauer class of period $n$ to a PU_{mn}-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.

29 pages, 4 figures

References in corpus (2)

• On the Cohomology of the Classifying Spaces of Projective Unitary Groups
• The topological period-index conjecture

Cited by in corpus (5)

• On the Cohomology of the Classifying Spaces of Projective Unitary Groups
• The Topological Period-Index Conjecture for spin${}^c$ 6-manifolds
• Some torsion classes in the Chow ring and cohomology of $BPG{L}_n$
• The cohomology of $BPU(p^m)$ and invariant polynomials
• Milnor operations and classifying spaces