Affordable Access

The Bing-Borsuk and the Busemann Conjectures

Authors
  • Halverson, Denise M.
  • Repovš, Dušan
Type
Published Article
Publication Date
Jan 10, 2009
Submission Date
Nov 06, 2008
Source
arXiv
License
Yellow
External links

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.

Report this publication

Statistics

Seen <100 times