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Speaker:

Holger Kammeyer
Affiliation:

Heinrich Heine Universität Düsseldorf
Date:

Mon, 13/05/2024 - 15:00 - 16:00
Location:

MPIM Lecture Hall $L^2$-Betti numbers capture free homology growth of a group along certain sequences of finite index normal subgroups. The question thus arises naturally if $L^2$-Betti can also be determined from the corresponding finite quotient groups. It turns out that the answer is "yes" in degree one and "no" in higher degrees as exhibited by $S$-arithmetic groups with CSP. We will explain, however, that Poitou-Tate duality in Galois cohomology shows that just enough information about the $L^2$-cohomology is contained in the finite quotient groups to determine the sign of the Euler characteristic. Joint work with G. Serafini.

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