We provide a smoothening criterion for group actions on manifolds by singular diffeomorphisms. We prove that if a countable group $\mathrm{\Gamma }$ has the fixed point property FW for walls (for example, if it has property $(T)$), every aperiodic action of $\mathrm{\Gamma }$ by diffeomorphisms that are of class $C^r$ with countably many singularities is conjugate to an action by true diffeomorphisms of class $C^r$ on a homeomorphic (possibly non‐diffeomorphic) manifold. As applications, we show that Navas's result for actions of Kazhdan groups on the circle, as well as the recent solutions to Zimmer's conjecture, generalise to aperiodic actions by diffeomorphisms with countably many singularities.

中文翻译：

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特性固件，可区分的结构和奇异动作的平滑性

我们通过奇异的亚纯性为流形上的群作用提供了一个平滑准则。我们证明如果一个可数的群体$\mathrm{\Gamma }$ 具有墙的定点属性FW（例如，如果具有属性） $（Ť）$）， $\mathrm{\Gamma }$ 通过类的同构 $C^{\mathrm{[R}}$ 具有许多奇点的类通过类的真微分同变与一个动作共轭 $C^{\mathrm{[R}}$在同胚（可能是非同胚）流形上。作为应用，我们证明了Navas对Kazhdan组在圆周上的作用的结果以及对Zimmer猜想的最新解决方案，通过具有许多奇异点的微分同构，推广到非周期性作用。