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

Holger Kammeyer; Roman Sauer

arxiv: 1804.10604 · v1 · pith:AZZGCOTYnew · submitted 2018-04-27 · 🧮 math.GR

S-arithmetic spinor groups with the same finite quotients and distinct ell²-cohomology

Holger Kammeyer , Roman Sauer This is my paper

classification 🧮 math.GR

keywords groupss-arithmeticarithmeticbetticohomologydistinctexamplesfinite

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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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S-arithmetic spinor groups with the same finite quotients and distinct ell²-cohomology

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