Kernels in measurable cohomology for transitive actions

2023/08/25 by Bucher, Michelle, Savini, Alessio
#22E41 #57T10 #FOS: Mathematics #Group Theory (math.GR) #K-Theory and Homology (math.KT)

paper · doi:10.48550/arxiv.2308.13335

Abstract

Given a connected semisimple Lie group G, Monod has recently proved that the measurable cohomology of the G-action H^*_m(G \curvearrowright G/P) on the Furstenberg boundary G/P, where P is a minimal parabolic subgroup, maps surjectively on the measurable cohomology of G through the evaluation on a fixed basepoint. Additionally, the kernel of this map depends entirely on the invariant cohomology of a maximal split torus. In this paper we show a similar result for a fixed subgroup L

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