Tue, 20 May 2025
15:00
15:00
L6
Cohomology of subgroups of SL2
Henrique Souza
Abstract
Given an FP-infinity subgroup G of SL(2,C), we are interested in the asymptotic behavior 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. We make no further assumptions on G, extending a previous result of W. Fu. 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).
As of this week, Friday's@2 is back for Hilary term, taking place as usual in L1 every Friday at 2pm, followed by tea, coffee and biscuits in the foyer.
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