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Mathematical Communications, Vol. 13 No. 2, 2008.

Original scientific paper

The Bing-Borsuk and the Busemann conjectures

Denise M. Halverson ; Department of Mathematics, Brigham Young University,Provo, U.S.A.
Dušan Repovš ; Faculty of Mathematics and Physics, and Faculty of Education, University of Ljubljana, Ljubljana, Slovenia

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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 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.

Keywords

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

Hrčak ID:

30884

URI

https://hrcak.srce.hr/30884

Publication date:

23.12.2008.

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