离散对称与紧凑的基本区，几何简单连通性-一个临时大纲的工作进展-
Discrete symmetry with compact fundamental domain, and geometric simple connectivity - A provisional Outline of work in Progress -
摘要：
我们证明了S. Brick和M. Mihalik，对于{ \ibf all}双递呈组$Γ$普遍成立。定义这一性质的一种方法是存在一个光滑紧致流形$M$，它具有$π_1 M = Γ$，使得$\tilde M$是几何单连通的（{ \it即}）。没有索引$λ= 1$的句柄）。也有替代的，更多的群体理论的定义，这是独立的表述。但是$Γ\in {\rm QSF}$不仅是一个普适性质，而且也是非常非平凡的;它对于$Γ= π_1 M^3$的非常特殊的情况（这里它意味着$π_1^{\infty} \tilde M^3 = 0$）实际上已经是已知的，作为G的一个推论。Perelman在三维流形的几何化上的重大突破。
英文摘要：
We show that a certain geometric property, the QSF introduced by S. Brick and M. Mihalik, is universally true for {\ibf all} finitely presented groups $Γ$. One way of defining this property is the existence of a smooth compact manifold $M$ with $π_1 M = Γ$, such that $\tilde M$ is geometrically simply-connected ({\it i.e.} without handles of index $λ= 1$). There are also alternative, more group-theoretical definitions, which are presentation independent. But $Γ\in {\rm QSF}$ is not only a universal property, it is quite highly non-trivial too; its very special case for $Γ= π_1 M^3$ (where it means $π_1^{\infty} \tilde M^3 = 0$) is actually already known, as a corollary of G. Perelman's big breakthrough on the Geometrization of 3-Manifolds.
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