Stabilization of Bounded Cohomology for Classical Groups

2022/01/11 by Carlos De la Cruz Mengual, Mengual, Carlos De la Cruz, Tobias Hartnick +1 · 2 citations
Mathematics · #11E57 #20G10 (Primary) #20G20 (Secondary) #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Group Theory (math.GR) #Homotopy and Cohomology in Algebraic Topology #K-Theory and Homology (math.KT)

paper · pdf · doi:10.48550/arxiv.2201.03879

openalex publication_date 2022/01/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that bounded cohomology stabilizes along sequences of classical Lie groups, and along sequences of lattices in them. Our method is based on a criterion from (arXiv:2307.12808) which adapts Quillen's stability method to the setting of bounded cohomology. This criterion is then applied to a family of measured complexes, the so-called Stiefel complexes, associated to any vector space endowed with a non-degenerate sesquilinear form.

Cited by

• Bounded cohomological induction for transverse measured groupoids
• A Quillen Stability Criterion for Bounded Cohomology

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