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arXiv · 1507.04915

The boundary model for the continuous cohomology of Isom$^+(\mathbb{H}^n)$

Hester Pieters
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Abstract

We prove that the continuous cohomology of $\text{Isom}^+(\mathbb{H}^n)$ can be measurably realized on the boundary of hyperbolic space. This implies in particular that for $\text{Isom}^+(\mathbb{H}^n)$ the comparison map from continuous bounded cohomology to continuous cohomology is injective in degree $3$. We furthermore prove a stability result for the continuous bounded cohomology of $\text{Isom}(\mathbb{H}^n)$ and $\text{Isom}(\mathbb{H}_{\mathbb{C}}^n)$.

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Hester Pieters. 2015-07-17. The boundary model for the continuous cohomology of Isom$^+(\mathbb{H}^n)$. https://arxiv.org/abs/1507.04915

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