A Cocycle Model for Topological and Lie Group Cohomology

Details A Cocycle Model for Topological and Lie Group Cohomology A Cocycle Model for Topological and Lie Group Cohomology

2011-10-14

arxiv.org/abs/1110.3304v2

Mathematics

Algebraic Topology

LaTeX, 32 pages; v2: relation to results of Schreiber added (Rem. IV.12), figures for the String Cocycle added (Ex. V.1)

Scientific paper

We propose a unified framework in which the different constructions of cohomology groups for topological and Lie groups can all be treated on equal footings. In particular, we show that the cohomology of "locally continuous" cochains (respectively "locally smooth" in the case of Lie groups) fits into this framework, which provides an easily accessible cocycle model for topological and Lie group cohomology. We illustrate the use of this unified framework and the relation between the different models in various applications. This includes the construction of cohomology classes characterizing the string group and a direct connection to Lie algebra cohomology.

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