Speaker: John Bryant
Abstract. A topological space X is homogeneous if, for every two points x and y in X, there is a homeomorphism that maps x to y. Topological groups and (connected) topological manifolds are among the more obvious examples. In 1965 Bing and Borsuk proved that, in dimensions 1 and 2, every locally compact, locally contractible homogeneous space is a topological manifold, and a conjecture arose that this should be true in higher dimensions as well. I will discuss the relationship of this conjecture to the topological classification of higher dimensional euclidean space resulting from work of R. Edwards, F. Quinn, and Bryant-Ferry-Mio-Weinberger and report on recent results of Bryant and Ferry showing that the Bing-Borsuk conjecture is false in dimensions greater than 5. In particular there are "nice" homogeneous spaces that are homotopy equivalent to the n-sphere (n larger than 5), that are nowhere locally euclidean.