The Degree-Three Bounded Cohomology of Complex Lie Groups of Classical Type

We determine the degree-three bounded cohomology of complex symplectic and orthogonal groups, completing the computation for complex Lie groups of classical type. A key ingredient is the "effectivization" of a bounded-cohomological stability theorem by Hartnick and the author. For this purpose, we exhibit a procedure that enables, under some circumstances, the improvement of an arbitrary cohomological stability range to an optimal one.