Papers › Computer proofs for Property (T), and SDP duality
Computer proofs for Property (T), and SDP duality
Martin Nitsche
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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,ℤ) and we prove that Aut(F₄) has property (T).
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