论文标题
属性的计算机证明（T）和SDP双重性
Computer proofs for Property (T), and SDP duality
论文作者
论文摘要
我们表明，Kazhdan财产的计算机证明（T）涉及的半决赛程序满足了强大的双重性，并且双重程序在谐波中具有几何解释。通过对共生的几何参数进行偶联，我们能够简化属性（t）SDP，如果它通过有限的内部自动形态携带对称性。作为一个应用程序，我们简化了$ sl（n，\ mathbb {z}）$的SDP证明，并证明$ aut（f_4）$具有属性（t）。
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).
