The Fourth Continuous Bounded Cohomology of the Complex Symplectic Group

Sixuan Gu, Yaoyu Cheng, Wei Qi

We prove that $H_{\mathrm{cb}}^4(\Sp(4,\CC);\RR)=0$. Together with Blatz's secondary stability and the rank-one theorem of Bucher--Savini, this gives degree-four vanishing for all…