Given a connected semisimple Lie group G, Monod (Trans. Amer. Math. Soc. B 144–159, 2022) has recently proved that the measurable cohomology of the G-action Hm∗(G↷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.
Bucher, M., Savini, A. (2025). Kernels in measurable cohomology for transitive actions. GEOMETRIAE DEDICATA, 219(3 (June 2025)), 1-18 [10.1007/s10711-025-01006-5].
Kernels in measurable cohomology for transitive actions
Savini, A.
2025
Abstract
Given a connected semisimple Lie group G, Monod (Trans. Amer. Math. Soc. B 144–159, 2022) has recently proved that the measurable cohomology of the G-action Hm∗(G↷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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