Cohomology of subgroups of SL2

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• Henrique Souza (Madrid)
• Friday 11 October 2024, 13:45-14:45
• MR13.

If you have a question about this talk, please contact Francesco Fournier-Facio.

Given an FP-infinity subgroup G of SL(2,C), we are interested in the asymptotic behaviour of the cohomology of G with coefficients in an irreducible complex representation V of SL(2,C). We prove that, as the dimension of V grows, the dimensions of these cohomology groups approximate the L2-Betti numbers of G. This yields a new method to compute those Betti numbers for finitely generated hyperbolic 3-manifold groups. We will give a brief idea of the proof, whose main tool is a completion of the universal enveloping algebra of the p-adic Lie algebra sl(2, Zp).

This talk is part of the Geometric Group Theory (GGT) Seminar series.

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