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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Inverse limits of topological group cohomologies


Author: Arnold J. Insel
Journal: Proc. Amer. Math. Soc. 55 (1976), 175-180
MSC: Primary 22D99; Secondary 18H10
DOI: https://doi.org/10.1090/S0002-9939-1976-0414784-6
MathSciNet review: 0414784
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Abstract: For second countable locally compact almost connected groups $ G$ and $ A$, where $ A$ is abelian and $ G$ acts on $ A$ continuously, it is shown that it is possible to represent $ A$ as an inverse limit of Lie groups $ \{ {A_n}\} $ compatible with the action of $ G$ and such that $ {H^{\ast}}(G,A)$ is isomorphic to $ {\lim _n}\operatorname{inv} {H^{\ast}}(G,{A_n})$, provided that $ A$ is compact or connected.


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DOI: https://doi.org/10.1090/S0002-9939-1976-0414784-6
Keywords: Inverse limit of Lie groups, topological group cohomologies
Article copyright: © Copyright 1976 American Mathematical Society