Bing-Borsuk猜想与Busemann猜想
The Bing-Borsuk and the Busemann Conjectures
摘要：
我们给出了两个关于流形特征的经典猜想：Bing Borsuk猜想断言每个$n$维齐次ANR是拓扑$n$ -流形，而Busemann猜想断言每个$n$维$G$ -空间是拓扑$n$ -流形.在这两种情况下的关键对象是所谓的{ \it广义流形}，即ENR同调流形。我们看看历史，从早期开始到现在。我们还列出了几个开放的问题和相关的插图。
英文摘要：
We present two classical conjectures concerning the characterization of manifolds: the Bing Borsuk Conjecture asserts that every $n$-dimensional homogeneous ANR is a topological $n$-manifold, whereas the Busemann Conjecture asserts that every $n$-dimensional $G$-space is a topological $n$-manifold. The key object in both cases are so-called {\it generalized manifolds}, i.e. ENR homology manifolds. We look at the history, from the early beginnings to the present day. We also list several open problems and related conjectures.
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