Abstract by Alex Safsten
Busemann spaces: the role of curvature and the infinite dimensional case
Busemann Geodesic spaces (g-spaces) are metric spaces endowed with a several properties which together guarantee the existence of geodesics. A long standing conjecture suggests that all g-spaces are manifolds. We show that g-spaces with locally bounded Alexandrov curvature do indeed posess manifold properties such as the existence of a local projection to a geodesic. We will present a standard definition for an infinite-dimensional metric space, and outline an unfinished argument for the non-existence of an infinite dimensional g-space.