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Groups, Geometry, and Dynamics


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Volume 14, Issue 3, 2020, pp. 857–869
DOI: 10.4171/GGD/566

Published online: 2020-10-12

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

Holger Kammeyer[1] and Roman Sauer[2]

(1) Karlsruhe Institute of Technology, Germany
(2) Karlsruhe Institute of Technology, Germany

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

Keywords: $\ell^2$-Betti numbers, profinite completion, $S$-arithmetic groups

Kammeyer Holger, Sauer Roman: $S$-arithmetic spinor groups with the same finite quotients and distinct $\ell^2$-cohomology. Groups Geom. Dyn. 14 (2020), 857-869. doi: 10.4171/GGD/566