Infinite CW-complexes, Brauer groups and phantom cohomology

被引：0

作者：

Hornbostel, Jens ^{[1
]}

Schroer, Stefan ^{[2
]}

机构：

[1] Berg Univ Wuppertal, Fachbereich C, D-42119 Wuppertal, Germany

[2] Heinrich Heine Univ, Math Inst, D-40204 Dusseldorf, Germany

来源：

ISRAEL JOURNAL OF MATHEMATICS | 2015年 / 207卷 / 01期

关键词：

HOMOLOGY; MAPS; CLASSIFICATION; SPACE;

D O I：

10.1007/s11856-015-1172-x

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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(a"currency sign/na"currency sign, 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.

引用

页码：77 / 101

页数：25