Euclidean-valued group cohomology is always reduced
Keyword(s):
Let [Formula: see text] be a topological field and [Formula: see text] a countable discrete group. Then for any linear [Formula: see text]-action on a finite-dimensional vector space over [Formula: see text], the groups of coboundaries in the inhomogeneous bar resolution are closed in all degrees, and hence the cohomology is reduced in all degrees. This can be deduced from a more general automatic-closure theorem for continuous linear transformations between inverse limits of finite-dimensional vector spaces.
1985 ◽
Vol 28
(3)
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pp. 319-331
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1993 ◽
Vol 45
(2)
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pp. 357-368
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1985 ◽
Vol 100
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pp. 123-138
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1990 ◽
Vol 49
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pp. 399-417
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1982 ◽
Vol 25
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pp. 133-139
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1995 ◽
Vol 138
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pp. 113-140
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