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Topology/Geometry Seminar

Finite quotients, arithmetic invariants, and hyperbolic volume

Yi Liu (Peking University)

Location:  Zoom
Date & time: Tuesday, 19 October 2021 at 11:00AM - 12:00PM

ABSTRACT: In this talk, I will discuss the question as to determine geometric properties of orientable closed hyperbolic 3-manifolds by the finite quotients of their fundamental groups. I will explain an approach to match up the (Zariski-dense algebraic) PSL_2 representations of a pair of those groups, up to conjugacy, if there is an isomorphism between their profinite completions. Assuming the p-adic Borel regulator injectivity conjecture, one may deduce that the hyperbolic volume, the invariant quaternion algebra, and the arithmeticity are profinite properties.

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