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 The K\"{u}nneth isomorphism in bounded cohomology preserving the norms Bull. Korean Math. Soc. 2020 Vol. 57, No. 4, 873-890 https://doi.org/10.4134/BKMS.b190547Published online February 13, 2020Printed July 31, 2020 HeeSook Park 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 $B^{\ast}(G) \widehat{\otimes} B^{\ast}(K)$ is isomorphic to the bounded cohomology $\widehat{H}^{\ast}(G \times K)$ of $G \times K$, which is the cohomology of $B^{\ast}(G \times K)$ as topological vector spaces, where $B^{\ast}(G)$ is a complex of bounded cochains of $G$ with real coefficients $\mathbb{R}$. In fact, we construct an isomorphism between these two cohomology groups that carries the canonical seminorm in $\widehat{H}^{\ast}(G \times K)$ to the seminorm in the cohomology of $B^{\ast}(G) \widehat{\otimes} B^{\ast}(K)$. Keywords : Bounded cohomology, resolution MSC numbers : Primary 55T99; Secondary 18G40 Downloads: Full-text PDF   Full-text HTML