Inducing spectral gaps for the cohomological Laplacians of Sp_2n(ℤ)

2025/04/23 by Mizerka, Piotr, Szymański, Jakub
#20G10 #FOS: Mathematics #Functional Analysis (math.FA) #Group Theory (math.GR) #Operator Algebras (math.OA)

paper · doi:10.48550/arxiv.2504.16625

Abstract

We show that the spectral gap of the first cohomological Laplacian Δ₁ for Sp_2n(ℤ) follows once a slightly stronger assumption holds for some Sp_2m(ℤ), where n≥ m. As an application of this result, we provide explicit lower bounds for some quotients of Sp_2n(ℤ) for any n≥ 2.

Citations

• Inducing spectral gaps for the cohomological Laplacians of SL_n(ℤ) and SAut(F_n)
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• Julia: A Fresh Approach to Numerical Computing
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