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 The Kunneth isomorphism in bounded cohomology preserving the norms Bull. Korean Math. Soc.Published online February 13, 2020 HeeSook Park Department of Mathematics Education, Sunchon National University Abstract : In this paper, for discrete groups G and K, we show that the cohomology of the complex of projective tensor product B*(G) and B*(K) is isomorphic to the bounded cohomology H*(G X K), which is the cohomology of the complex B*(G X K), as topological vector spaces, where B*(G) is a complex of bounded cochains of G with real coefficients R. In fact, we construct an isomorphism between these two cohomology groups that carries the canonical seminorm in the bounded cohomology H*(G X K) to the seminorm in the cohomology of the complex of projective tensor product B*(G) and B*(K). Keywords : bounded cohomology MSC numbers : Primary: 55T99, Secondary: 18G40} Full-Text :