Infinite CW-complexes, Brauer groups and phantom cohomology

2013/04/15 by Jens Hornbostel, Hornbostel, Jens, Stefan Schroeer +1
Mathematics · #14F22 #16K50 #55N10 #Algebraic Geometry (math.AG) #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #FOS: Mathematics #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #math.AG #math.AT #msc:14F22 #msc:16K50 #msc:55N10

paper · pdf · doi:10.48550/arxiv.1304.3986

Paper reorganized by dissolving former Section 4, reference added, otherwise minor changes. 18 pages. To appear in Israel J. Math

openalex publication_date 2013/04/15 · arxiv created 2013/09/10 · arxiv updated 2013/09/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Expanding a result of Serre on finite CW-complexes, we show that the Brauer group coincides with the cohomological Brauer group for arbitrary compact spaces. Using results from the homotopy theory of classifying spaces for Lie groups, we give another proof of the result of Antieau and Williams that equality does not hold for Eilenberg--MacLane spaces of type K(Z/nZ,2). Employing a result of Dwyer and Zabrodsky, we show the same for the classifying spaces BG where G is an infinite-dimensional F_p-vector space. In this context, we also give a formula expressing phantom cohomology in terms of homology.

Citations

• On the classification of oriented 3-plane bundles over a 6-complex

Related

• Homotopy- and Cohomology Groups of Kan Complexes
• Brauer groups and étale homotopy type
• Cohomological uniqueness of some p-groups
• Equivariant Phantom maps
• The Burnside Ring and Equivariant Stable Cohomotopy for Infinite Groups