A cocycle model for topological and Lie group cohomology
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- by Friedrich Wagemann and Christoph Wockel PDF
- Trans. Amer. Math. Soc. 367 (2015), 1871-1909
Abstract:
We propose a unified framework in which the different constructions of cohomology groups for topological and Lie groups can all be treated on an equal footing. 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.References
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Additional Information
- Friedrich Wagemann
- Affiliation: Laboratoire de Mathématiques Jean Leray, UMR 6629 du CNRS, Université de Nantes, F-44322 Nantes Cedex 3, France
- Email: wagemann@math.univ-nantes.fr
- Christoph Wockel
- Affiliation: Department of Mathematics, University of Hamburg, Bundesstrasse 55, 20146 Hamburg, Germany
- Email: christoph@wockel.eu
- Received by editor(s): January 16, 2012
- Received by editor(s) in revised form: February 11, 2013
- Published electronically: September 4, 2014
- © Copyright 2014 by the authors
- Journal: Trans. Amer. Math. Soc. 367 (2015), 1871-1909
- MSC (2010): Primary 22E41; Secondary 57T10, 20J06
- DOI: https://doi.org/10.1090/S0002-9947-2014-06107-2
- MathSciNet review: 3286502