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Profiniteness of higher rank volume

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arxiv 2412.13056 v1 pith:3VIXFBNC submitted 2024-12-17 math.GR

Holger Kammeyer , Steffen Kionke , Ralf Köhl This is my paper · ORCID
classification math.GR
keywords congruencehigherprofiniterankvolumeadditionallycompletioncovolume
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We show that the covolume of an irreducible lattice in a higher rank semisimple Lie group with the congruence subgroup property is determined by the profinite completion. Without relying on CSP, we additionally show that volume is a profinite invariant of octonionic hyperbolic congruence manifolds.

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  1. Infinite groups from the profinite point of view

    math.GR 2025-06 accept novelty 1.0 of 10

    This survey of profinite group completions shows which group properties are determined by the set of finite quotients, collecting both negative examples and positive results.

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