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

arXiv eprints
 Pub Date:
 July 2022
 DOI:
 10.48550/arXiv.2207.02783
 arXiv:
 arXiv:2207.02783
 Bibcode:
 2022arXiv220702783K
 Keywords:

 Mathematics  Group Theory;
 Mathematics  Operator Algebras