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[Текст] : монография / K.H. Hofmann, P.S. Mostert. - Berlin : VEB DEUTSCHER VERLAG DER WISSENSCHAFTEN, 1973. - 236 с. + List of notation p. 232-234, Subject Index p. 235-236. - With an appendix by E.C. Nummela Bibliogr. p. 229-231 . - 17.82 р.
Аннотация: Of all topological algebraic structures compact topological groups have perheps the richest theory since so many different fields contribute to their study: Analysis enters through the representation theory and harmonic analysis; differential geometry, the theory of real analytic functions and the theory of differential equations come into the play via Lie group theory; point set topology is used in describing the local geometric structure of compact groups via limit spaces ; global topology and the theory of manifolds again play a role through Lie group theory; and, of course, algebra enters through the cohomology and homology theory. A particularly well understood subclass of compact groups is the class of compact abelian groups. An added element of elegance is the duality theory, which stated that the category of compact abelian groups is completely equivalent to the category of (discrete) abelian groups with all arrows reversed. This allows for a virtually complete algebraisation of any question concerning compact abelian groups. The subclass of compact abelian groups is not so special within the category of compact groups as it may seem at first glance. As is very well known, the local geometry structure of a compact group may be extremely complicated, but all local complication happens to be "abelian". All of these features qualify the category of compact abelian groups as a very suitable test category for the applicability of various tools; a tool which does not work rather explicitly in the category of compact abelian groups is not likely tobe very usefulin the more general circumstances of arbitrary compact or even more general topological groups. The present monograph is an essay to test the tools of cohomology on the category of compact abelian groups. The usefulness of cohomology does not need, of course, any corroboration.No comprehensive study of the explicit nature of the cohomology functor on this category has, however, been undertaken untill now. The current treatise attempts to fill this gap.

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ИВМ СО РАН : 660036, Красноярск, Академгородок, 50, стр.44

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Mostert, P.S.
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