Measurable bounded cohomology of $t$-discrete measured groupoids via resolutions

Filippo Sarti; Alessio Savini

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arXiv · 2503.22350

Measurable bounded cohomology of $t$-discrete measured groupoids via resolutions

Filippo Sarti·Alessio Savini

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Abstract

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 $\mathcal{G}$ can be computed using any amenable $\mathcal{G}$-space. In particular, we can compute bounded cohomology using strong boundaries.

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Filippo Sarti, Alessio Savini. 2025-03-28. Measurable bounded cohomology of $t$-discrete measured groupoids via resolutions. https://arxiv.org/abs/2503.22350

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