Nicolas Monod
Published 2020-11-24Version 1
We prove that the cohomology of semi-simple Lie groups admits boundary values, which are measurable cocycles on the Furstenberg boundary. This generalises known invariants such as the Maslov index on Shilov boundaries, the Euler class on projective space, or the hyperbolic ideal volume on spheres. In rank one, this leads to an isomorphism between the cohomology of the group and of this boundary model. In higher rank, additional classes appear, which we determine completely.
Two results on cohomology of groups adapted to cochains
Enumeration of nilpotent loops via cohomology
Groups with the same cohomology as their pro-$p$ completions
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