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

Hester Pieters

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

Group Theory 2019-02-05 v2 Algebraic Topology

Authors: Hester Pieters

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 $\text{Isom}(\mathbb{H}_{\mathbb{C}}^n)$ .

Keywords

continuous cohomology Isom$^+(\mathbb{H}^n)$ boundary model hyperbolic space continuous bounded cohomology comparison map stability result

Cite

@article{arxiv.1507.04915,
  title  = {The boundary model for the continuous cohomology of Isom$^+(\mathbb{H}^n)$},
  author = {Hester Pieters},
  journal= {arXiv preprint arXiv:1507.04915},
  year   = {2019}
}

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25 pages, 1 figure, changed title, revised and extended version

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

Abstract

Keywords

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