Diff^r_+(S^n) is boundedly acyclic for n≥4 and 1≤r≤∞, so all positive-degree classes in its discrete bounded cohomology vanish.
Lamplighters and the bounded cohomology of T hompson's group
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Bounded cohomology of diffeomorphism groups of higher dimensional spheres
Diff^r_+(S^n) is boundedly acyclic for n≥4 and 1≤r≤∞, so all positive-degree classes in its discrete bounded cohomology vanish.