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We establish Monod's isomorphism conjecture in degree-three boundedcohomology for every complex simple Lie group of classical type. Our mainingredient is a bounded-cohomological stability theorem with an optimal rangein degree three that we bootstrap from previous stability results by the authorand Hartnick. The bootstrapping procedure relies on the occurrence in oursetting of a variant of the recently observed phenomenon of secondary stabilityin the sense of Galatius--Kupers--Randal-Williams.

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