1. The Bing-Borsuk and the Busemann conjectures
- Author
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Halverson, Dm and Dušan Repovš
- Subjects
Mathematics - Differential Geometry ,Mathematics - Geometric Topology ,57N75 ,57N15 ,53C70 ,57P99 ,Mathematics::Differential Geometry ,Mathematics::Symplectic Geometry ,Mathematics::Geometric Topology ,Bing-Borsuk conjecture ,homogeneity ,ANR ,Busemann G-space ,Busemann conjecture ,Moore conjecture ,de Groot conjecture ,generalized manifold ,cell-like resolution ,general position property ,delta embedding property ,disjoint disks property ,recognition - Abstract
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., Comment: We have corrected three small typos on pages 8 and 9
- Published
- 2008