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arXiv · 2009.05134

Computer proofs for Property (T), and SDP duality

Martin Nitsche
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Abstract

We show that the semidefinite programs involved in the computer proofs for Kazhdan's property (T) satisfy strong duality and that the dual programs have a geometric interpretation in terms of harmonic cocycles. By dualizing geometric arguments about cocycles, we are able to simplify the property (T) SDP in the case where it carries a symmetry by finite-order inner automorphisms. As an application, we simplify the SDP proof for $SL(n,\mathbb{Z})$ and we prove that $Aut(F_4)$ has property (T).

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Martin Nitsche. 2020-09-10. Computer proofs for Property (T), and SDP duality. https://arxiv.org/abs/2009.05134

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