The Bing-Borsuk and the Busemann Conjectures

Details The Bing-Borsuk and the Busemann Conjectures The Bing-Borsuk and the Busemann Conjectures

2008-11-06

arxiv.org/abs/0811.0886v2

Math. Comm. 13:2 (2008), 163-184

Mathematics

Geometric Topology

We have corrected three small typos on pages 8 and 9

Scientific paper

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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