On discontinuities of cocycles in cohomology theories for topological groups

Details On discontinuities of cocycles in cohomology theories for topological groups On discontinuities of cocycles in cohomology theories for topological groups

2011-12-07

arxiv.org/abs/1112.1465v1

Mathematics

Group Theory

30 pages, 2 figures

Scientific paper

This paper studies classes in Moore's measurable cohomology theory for locally compact groups and Polish modules. An elementary dimension-shifting argument is used to show that all such classes have representatives with considerable extra topological structure beyond measurability. Based on this idea, for certain target modules one can also construct a direct comparison map with a different cohomology theory for topological groups defined by Segal, and show that this map is an isomorphism.

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