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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

   
 

 

A cocycle model for topological and Lie group cohomology


Authors: Friedrich Wagemann and Christoph Wockel
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
Published electronically: September 4, 2014
MathSciNet review: 3286502
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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.


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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

DOI: https://doi.org/10.1090/S0002-9947-2014-06107-2
Keywords: Cohomology for topological groups, cohomology for Lie groups, abelian extension, crossed module, Lie algebra cohomology, string group
Received by editor(s): January 16, 2012
Received by editor(s) in revised form: February 11, 2013
Published electronically: September 4, 2014
Article copyright: © Copyright 2014 by the authors