A splitting theorem for nonnegatively curved Alexandrov spaces ABSTRACT: This talk is about compact nonnegatively curved Alexandrov spaces whose boundaries decompose into several components, called strata. In positive curvature, k strata always intersect as long as k does not exceed the space's dimension. In nonnegative curvature this is not true, since taking products produces counterexamples. We show that these are the only counterexamples, in other words: If not all strata intersect, the space splits as a metric product.