Year: 2026
Type: preprint
Abstract: 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 complex symplectic and odd complex orthogonal groups. In normalized symplectic Gram coordinates, we establish a bounded-primitive estimate and compute the measurable cohomology of the projective action. An explicit rational cocycle has divergent periods on a family of finite orbit cycles of uniformly bounded $\ell^1$-mass. A two-cone averaging construction extends the period estimate to measurable cochains and excludes bounded representatives of every nonzero degree-four measurable action class.
Source: arXiv (Cornell University)
Authors: Gu, Sixuan, Cheng, Yaoyu, Qi, Wei
Institutions: Chinese University of Hong Kong, The Ohio State University
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7213422288