Residual finiteness of extensions of arithmetic subgroups of SU(d,1) with cusps

2022/03/28 by Richard Hill, Hill, Richard M.
Mathematics · #Geometric and Algebraic Topology #Finite Group Theory Research #Advanced Algebra and Geometry

paper · pdf · doi:10.48550/arxiv.2203.14793

Abstract

Let Γ be an arithmetic subgroup of SU(d,1) with cusps, and let X_Γ be the associated locally symmetric space. We prove that if the first inner cohomology group H¹_!(X_Γ,ℂ) is non-zero then the pre-image of Γ in each connected cover of SU(d,1) is residually finite. We also give an example of a such a group Γ for which H¹_!(X_Γ,ℂ) is non-zero.

Related

• Residual finiteness for central extensions of lattices in\n \PU(n,1) and negatively curved projective varieties
• Residual finiteness of some automorphism groups of high dimensional manifolds
• Weak Weyl's law for congruence subgroups
• Non-stable groups
• Non-residually finite extensions of arithmetic groups