Geodesic
Bounded cohomology is not a profinite invariant
Canadian mathematical bulletin, Tome 67 (2024) no. 2, pp. 379-390

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DOI

We construct pairs of residually finite groups with isomorphic profinite completions such that one has non-vanishing and the other has vanishing real second bounded cohomology. The examples are lattices in different higher-rank simple Lie groups. Using Galois cohomology, we actually show that $\operatorname {SO}^0(n,2)$ for $n \ge 6$ and the exceptional groups $E_{6(-14)}$ and $E_{7(-25)}$ constitute the complete list of higher-rank Lie groups admitting such examples.
DOI : 10.4153/S0008439523000826
Mots-clés : Profinite invariance, bounded cohomology, lattices in Lie groups 
Echtler, Daniel; Kammeyer, Holger. Bounded cohomology is not a profinite invariant. Canadian mathematical bulletin, Tome 67 (2024) no. 2, pp. 379-390. doi: 10.4153/S0008439523000826
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     title = {Bounded cohomology is not a profinite invariant},
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     pages = {379--390},
     year = {2024},
     volume = {67},
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     doi = {10.4153/S0008439523000826},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/S0008439523000826/}
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