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

Holger Kammeyer; Roman Sauer

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arXiv · 1804.10604

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

Holger Kammeyer·Roman Sauer

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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 $\ell^2$-Betti number is not a profinite invariant for all $i \ge 2$.

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Holger Kammeyer, Roman Sauer. 2018-04-27. S-arithmetic spinor groups with the same finite quotients and distinct $\ell^2$-cohomology. https://arxiv.org/abs/1804.10604

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