The Degree-Three Bounded Cohomology of Complex Lie Groups of Classical Type

2023/04/02 by Carlos De la Cruz Mengual, Mengual, Carlos De la Cruz · 2 citations
Mathematics · #20F65 (Secondary) #20G10 (Primary) #20J05 #FOS: Mathematics #Geometric and Algebraic Topology #Geometry and complex manifolds #Group Theory (math.GR) #Homotopy and Cohomology in Algebraic Topology #K-Theory and Homology (math.KT)

paper · pdf · doi:10.48550/arxiv.2304.00607

openalex publication_date 2023/04/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We establish Monod's isomorphism conjecture in degree-three bounded cohomology for every complex simple Lie group of classical type. Our main ingredient is a bounded-cohomological stability theorem with an optimal range in degree three that we bootstrap from previous stability results by the author and Hartnick. The bootstrapping procedure relies on the occurrence in our setting of a variant of the recently observed phenomenon of secondary stability in the sense of Galatius--Kupers--Randal-Williams.

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