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Some remarks on acyclicity in bounded cohomology
We show that a surjective homomorphism $\varphi \colon \Gamma \to K$ of (discrete) groups induces an isomorphism $H^\bullet_b(K; V) \to H^\bullet_b(\Gamma; \varphi^{-1} V)$ in bounded cohomology for all dual normed $K$-modules $V$ if and only if the kernel of $\varphi$ is boundedly acyclic. This complements a previous result by the …