We show that the cohomological Laplacian in degree 1 in the group cohomology of SL3(Z) is a sum of hermitian squares in the algebra Mn(RG). We provide an estimate of the spectral gap for this Laplacian for every unitary representation. Our results have been obtained by convex optimization technique of semidefinite programming (SDP).
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Kaluba et al. (2024) studied this question.
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