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A Cocycle Model for Topological and Lie Group Cohomology

Authors
  • Wagemann, Friedrich
  • Wockel, Christoph
Type
Preprint
Publication Date
Feb 13, 2013
Submission Date
Oct 14, 2011
Identifiers
arXiv ID: 1110.3304
Source
arXiv
License
Yellow
External links

Abstract

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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