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merged little left-over material from what is now Pontryagin duality > history into here (just one reference and a list of “Related concepts”)
added pointer to the original:
Lev Pontrjagin, Theory of topological commutative groups, Uspekhi Mat. Nauk, 1936, no. 2, 177–195 (mathnet:umn8882)
English translation: Annals of Mathematics Second Series, Vol. 35, No. 2 (Apr., 1934), pp. 361-388 (doi:10.2307/1968438)
[edit: Hm, the dates suggest that the Russian version is actually translated from an English original? ]
added mentioning of the following example (here):
For $G$ a finite group, the fundamental group $\pi_1(-)$ of the $G$-fixed locus $(-)^G$ of the base space $\mathcal{B} PU(\mathcal{H})$ of the universal equivariant $PU(\mathbb{H})$-bundle (classifying 3-twists in twisted equivariant K-theory) is
$\pi_1 \Big( \big( \mathcal{B} PU(\mathcal{H}) \big)^G \Big) \;\simeq\; Grps(G, S^1) \,=\, \widehat G$(in any connected component of a “stable map” $G \to PU(\mathcal{H})$, that is) and hence is the Pontrjagin dual group when $G$ is abelian.
Re #5:
[edit: Hm, the dates suggest that the Russian version is actually translated from an English original? ]
Yes, the Russian version explicitly says so in the first footnote. It also says that Chapter II was completely rewritten in the Russian translation, though.
[ obsolete ]
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