Abstract
In this paper we give a new approach to the theory of bounded cohomology. The ideas of relative homological algebra, modified so that they are based on a natural seminorm in the bounded cohomology, play a central role in this approach. Moreover, a new proof is given of the vanishing theorem in the bounded cohomology of simply connected spaces, and also an analog of Leray's theorem on coverings in the theory of bounded cohomology.
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Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 143, pp. 69–109, 1985.
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Ivanov, N.V. Foundations of the theory of bounded cohomology. J Math Sci 37, 1090–1115 (1987). https://doi.org/10.1007/BF01086634
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DOI: https://doi.org/10.1007/BF01086634