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arXiv · 2207.02783

Spectral gap for the cohomological Laplacian of $\operatorname{SL}_3(\mathbb{Z})$

Marek Kaluba·Piotr Mizerka·Piotr W. Nowak
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Abstract

We show that the cohomological Laplacian in degree 1 in the group cohomology of $\operatorname{SL}_3(\mathbb{Z})$ is a sum of hermitian squares in the algebra $\mathbb{M}_n(\mathbb{R}G)$. We provide an estimate of the spectral gap for this Laplacian for every unitary representation.

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Marek Kaluba, Piotr Mizerka, Piotr W. Nowak. 2022-07-06. Spectral gap for the cohomological Laplacian of $\operatorname{SL}_3(\mathbb{Z})$. https://arxiv.org/abs/2207.02783

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