Izvorni znanstveni članak

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

Sažetak

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.

Ključne riječi

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

Datum izdavanja:

23.12.2008.

Posjeta: 3.487 *