15:00
Cohomology of subgroups of SL2
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.
Registration for this year's conference for women and non-binary people in Maths is now open - sign up here. Lead, Learn, and Make a Difference as an Oxford Laidlaw Scholar!
Open to first-year undergraduates, this 18-month programme combines leadership training, research, and community impact projects to drive meaningful change with an annual stipend to support your journey. Applications close 3rd Feb 2025.
Five Arrows, the alternative investment arm of Rothschild & Co, is looking to hire graduates for their Corporate Private Equity Graduate Programme. If you are interested, please apply by 18th February 2025.
Preference will be given to candidates in their final year of study of an undergraduate or master’s programme, who would be available to start work in July 2025 / January 2026.