2025/03/28 by Filippo Sarti, Sarti, Filippo, Alessio Savini +1 · 1 citation
Computer Science · Mathematics · #Advanced Operator Algebra Research #Algebra over a field #Algebraic Topology (math.AT) #Bounded function #Cohomology #De Rham cohomology #Derived category #Dynamical Systems (math.DS) #FOS: Mathematics #Functional Analysis (math.FA) #Group cohomology #Homotopy and Cohomology in Algebraic Topology #Spectrum (functional analysis) #Topological and Geometric Data Analysis
paper · pdf · doi:10.48550/arxiv.2503.22350
openalex publication_date 2025/03/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We define bounded cohomology of t-discrete measured groupoids with coefficients into measurable bundles of Banach spaces. Our approach via homological algebra extends the classic theory developed by Ivanov and by Monod. As a consequence, we show that the bounded cohomology of a t-discrete groupoid G can be computed using any amenable G-space. In particular, we can compute bounded cohomology using strong boundaries.