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Computer proofs for Property (T), and SDP duality

Martin Nitsche
arXiv: Group Theory
Sep 2020
摘要
We show that the semidefinite programs involved in the computer proofs for Kazhdan's Property (T) satisfy strong duality, and that the dual problem has a geometric interpretation similar to Property (FH). Using SDP duality, we simplify the SDP proof for $SL(n,\mathbb{Z})$ to an almost humanly computable level. We also give a relatively fast SDP proof for $Aut(F_n)$, $n\geq 4$.
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