Abstract:

The classification of manifolds with a lower sectional curvature bound is an open and difficult problem. The symmetry program seeks to simplify the problem by additionally assuming some "large" amount of symmetries, then gradually reducing these assumptions. Along these lines, this talk discusses a classification of almost non-negatively curved, simply connected, closed 5-manifolds which admit an isometric and effective $T^2$-action. This is joint work with John Harvey and Catherine Searle.