Abstract：

Alexandrov spaces (with curvature bounded below) are metric generalizations of complete Riemannian manifolds with a uniform lower sectional curvature bound. Instances of Alexandrov spaces include compact Riemannian orbifolds and orbit spaces of isometric compact Lie group actions on compact Riemannian manifolds. In addition to being objects of intrinsic interest, Alexandrov spaces play an important role in Riemannian geometry, for example, in Perelman's proof of the Poincaré Conjecture. In this talk, I will discuss the topology and geometry of 3-dimensional Alexandrov spaces, focusing on extensions of basic results in 3-manifold topology (such as the prime decomposition theorem) to general three-dimensional Alexandrov spaces. This is joint work with Luis Atzin Franco Reyna, José Carlos Gómez-Larrañaga, Luis Guijarro, and Wolfgang Heil.