The Cannon Conjecture for a torsion‐free hyperbolic group $G$ with boundary homeomorphic to $S^2$ says that $G$ is the fundamental group of an aspherical closed 3‐manifold $M$. It is known that then $M$ is a hyperbolic 3‐manifold. We prove the stable version that for any closed manifold $N$ of dimension greater or equal to 2 there exists a closed manifold $M$ together with a simple homotopy equivalence $M\to N\times BG$. If $N$ is aspherical and ${\pi }_1(N)$ satisfies the Farrell–Jones Conjecture, then $M$ is unique up to homeomorphism.

中文翻译：

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关于稳定的Cannon猜想

无扭转双曲群的Cannon猜想 $G$ 边界同胚 ${\mathrm{小号}}^2$ 说 $G$ 是非球面封闭三流形的基本群 $\mathrm{中号}$。众所周知$\mathrm{中号}$是双曲3流形。我们证明了适用于任何封闭歧管的稳定版本$ñ$ 尺寸大于或等于2时，存在一个封闭的歧管 $\mathrm{中号}$ 以及简单的同伦对等 $\mathrm{中号}\to ñ\times 乙G$。如果$ñ$ 是非球面的 ${\pi }_{\mathrm{1个}}（ñ）$ 满足Farrell-Jones猜想，然后 $\mathrm{中号}$ 直到同胚为止是唯一的。