Denise Halverson, Two famous manifold recognition problems in topology

Abstract. Two classical conjectures concerning the characterization of manifolds will be presented: 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. We will look at the history, from the early beginnings to the present day. We will also list several open problems and related conjectures.