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Residual finiteness and discrete subgroups of Lie groups

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arxiv 2407.07680 v2 pith:7AAPO6GE submitted 2024-07-10 math.GR math.GTmath.NT

Matthew Stover This is my paper · ORCID
classification math.GRmath.GTmath.NT
keywords discretegammaansweranswerscompletedescribesfairlyfinite
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abstract

Let $G$ be a real Lie group and $\Gamma < G$ be a discrete subgroup of $G$. Is $\Gamma$ residually finite? This paper describes known positive and negative results then poses some questions whose answers will lead to a fairly complete answer for lattices.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Cohomological nonvanishing for algebraic fundamental groups of ball quotients

    math.AG 2025-08 accept novelty 7.0 of 10

    For cocompact arithmetic lattices of simplest type in PU(n,1), the cohomology of the profinite completion is nontrivial up to degree 2n for large primes.

  2. Hyperlinearity, stability and asymptotic spectral gap of higher rank lattices

    math.GR 2025-06 conditional novelty 7.0 of 10

    For higher-rank lattices, Hilbert-Schmidt stability implies non-hyperlinearity of certain central extensions, and character rigidity is equivalent to hyperfinite Hilbert-Schmidt stability.

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