Algebraic cohomology of topological groups

Wigner, David

doi:10.1090/S0002-9947-1973-0338132-7

Algebraic cohomology of topological groups
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by David Wigner

Trans. Amer. Math. Soc. 178 (1973), 83-93

DOI: https://doi.org/10.1090/S0002-9947-1973-0338132-7

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Abstract:

A general cohomology theory for topological groups is described, and shown to coincide with the theories of C. C. Moore [12] and other authors. We also recover some invariants from algebraic topology.

References

Glen E. Bredon, Sheaf theory, McGraw-Hill Book Co., New York-Toronto-London, 1967. MR 0221500

Separability, metrizability, completeness and extensions of topological groups

David A. Buchsbaum, Satellites and universal functors, Ann. of Math. (2) 71 (1960), 199–209. MR 112905, DOI 10.2307/1970081
Jacques Dixmier and Adrien Douady, Champs continus d’espaces hilbertiens et de $C^{\ast }$-algèbres, Bull. Soc. Math. France 91 (1963), 227–284 (French). MR 163182, DOI 10.24033/bsmf.1596

Cohomologies des groupes compacts totalement discontinues

23

W. T. van Est, Group cohomology and Lie algebra cohomology in Lie groups. I, II, Nederl. Akad. Wetensch. Proc. Ser. A. 56 = Indagationes Math. 15 (1953), 484–492, 493–504. MR 0059285, DOI 10.1016/S1385-7258(53)50061-7
G. Hochschild and G. D. Mostow, Cohomology of Lie groups, Illinois J. Math. 6 (1962), 367–401. MR 147577, DOI 10.1215/ijm/1255632500
J.-L. Koszul, Multiplicateurs et classes caractéristiques, Trans. Amer. Math. Soc. 89 (1958), 256–266 (French). MR 99660, DOI 10.1090/S0002-9947-1958-0099660-7
Saunders Mac Lane, Homology, Die Grundlehren der mathematischen Wissenschaften, Band 114, Academic Press, Inc., Publishers, New York; Springer-Verlag, Berlin-Göttingen-Heidelberg, 1963. MR 0156879, DOI 10.1007/978-3-642-62029-4
Ernest Michael, Continuous selections. II, Ann. of Math. (2) 64 (1956), 562–580. MR 80909, DOI 10.2307/1969603
John Milnor, Construction of universal bundles. I, Ann. of Math. (2) 63 (1956), 272–284. MR 77122, DOI 10.2307/1969609
Calvin C. Moore, Extensions and low dimensional cohomology theory of locally compact groups. I, II, Trans. Amer. Math. Soc. 113 (1964), 40–63; ibid. 113 (1964), 64–86. MR 171880, DOI 10.1090/S0002-9947-1964-0171880-5

Continuous groups

1

Extensions de groupes localement compacts (d’après Iwasawa et Gleason)

28

David Wigner, Algebraic cohomology of topological groups, Bull. Amer. Math. Soc. 76 (1970), 825–826. MR 263975, DOI 10.1090/S0002-9904-1970-12569-1
Nobuo Yoneda, On Ext and exact sequences, J. Fac. Sci. Univ. Tokyo Sect. I 8 (1960), 507–576 (1960). MR 225854