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arXiv · 2305.18904

Bounded cohomology is not a profinite invariant

Daniel Echtler·Holger Kammeyer
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Abstract

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.

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Daniel Echtler, Holger Kammeyer. 2023-05-30. Bounded cohomology is not a profinite invariant. https://doi.org/10.4153/s0008439523000826

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