论文标题
关于布朗的问题，庞加雷的模型用于适当动作的分类空间和尼尔森实现
On Brown's Problem, Poincare' models for the classifying spaces for proper actions and Nielsen Realization
论文作者
论文摘要
存在一个问题，是否对于给定的无扭转离散组$γ$是否存在相同的拓扑拓扑$γ$ - manifold，这是等效的同性恋，等同于分类空间的适当操作。它与尼尔森的实现和布朗的问题有关，如果基础群体实际上具有同胞d维空间，是否有针对适当动作的d维模型。假设预期的歧管模型具有零维奇异集，我们在庞加莱类别中解决了问题，并在某些条件下与基础群体有关，例如，如果它是多重的，则获得有关布朗问题的新结果。在与詹姆斯·戴维斯（James Davis）的续集论文中，我们将处理这个 在拓扑歧管的水平上。
There is the problem, whether for a given virtually torsionfree discrete group $Γ$ there exists a cocompact proper topological $Γ$-manifold, which is equivariantly homotopy equivalent to the classifying space for proper actions. It is related to Nielsen's Realization and to the problem of Brown, whether there is a d-dimensional model for the classifying space for proper actions, if the underlying group has virtually cohomological dimension d. Assuming that the expected manifold model has a zero-dimensional singular set, we solve the problem in the Poincaré category and obtain new results about Brown's problem under certain conditions concerning the underlying group, for instance if it is hyperbolic. In a sequel paper together with James Davis we will deal with this on the level of topological manifolds.
