Geodesic
The boundary model for the continuous cohomology of Isom$^+ (\mathbb H^n)$
Hester Pieters1
1Technion - Israel Institute of Technology, Haifa, Israel
Groups, geometry, and dynamics, Tome 12 (2018) no. 4, pp. 1239-1263

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DOI

We prove that the continuous cohomology of Isom+(Hn) can be measurably realized on the boundary of hyperbolic space. This implies in particular that for Isom+(Hn) 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 Isom(Hn) and Isom(HCn​).
DOI : 10.4171/ggd/470
Classification : 20-XX, 22-XX, 46-XX, 53-XX
Mots-clés : Continuous group cohomology, continuous bounded cohomology, hyperbolic spaces, measurable cohomology

Hester Pieters  1

1 Technion - Israel Institute of Technology, Haifa, Israel 
Hester Pieters. The boundary model for the continuous cohomology of Isom$^+ (\mathbb H^n)$. Groups, geometry, and dynamics, Tome 12 (2018) no. 4, pp. 1239-1263. doi: 10.4171/ggd/470
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     pages = {1239--1263},
     year = {2018},
     volume = {12},
     number = {4},
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     url = {http://geodesic.mathdoc.fr/articles/10.4171/ggd/470/}
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