The Bing-Borsuk and the Busemann Conjectures

Denise M. Halverson; Dušan Repovš

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arXiv · 0811.0886

The Bing-Borsuk and the Busemann Conjectures

Denise M. Halverson·Dušan Repovš

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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.

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BibTeX RIS

Denise M. Halverson, Dušan Repovš. 2009-01-10. The Bing-Borsuk and the Busemann Conjectures. https://arxiv.org/abs/0811.0886

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