$S$-arithmetic spinor groups with the same finite quotients and distinct $\ell^2$-cohomology

Holger Kammeyer; Roman Sauer

doi:10.4171/ggd/566

JournalsggdVol. 14, No. 3pp. 857–869

$S$ -arithmetic spinor groups with the same finite quotients and distinct $ℓ^{2}$ -cohomology

Holger Kammeyer
Karlsruhe Institute of Technology, Germany
Roman Sauer
Karlsruhe Institute of Technology, Germany

$$S$-arithmetic spinor groups with the same finite quotients and distinct $\ell^2$-cohomology cover$

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Abstract

In this note we refine examples by Aka from arithmetic to $S$ -arithmetic groups to show that the vanishing of the $i$ -th $ℓ^{2}$ -Betti number is not a profinite invariant for all $i \geq 2$ .

Cite this article

Holger Kammeyer, Roman Sauer, $S$ -arithmetic spinor groups with the same finite quotients and distinct $ℓ^{2}$ -cohomology. Groups Geom. Dyn. 14 (2020), no. 3, pp. 857–869

DOI 10.4171/GGD/566