Gromov and Ivanov established an analogue of Leray’s theorem on cohomology of contractible covers for bounded cohomology of amenable covers. We present an alternative proof of this fact, using classifying spaces of families of subgroups.
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C. Löh, Roman Sauer, Bounded cohomology of amenable covers via classifying spaces. Enseign. Math. 66 (2020), no. 1/2, pp. 151–172DOI 10.4171/LEM/66-1/2-8