Torus actions, maximality, and non-negative curvature

Geometry/topology Seminar

Catherine Searle (Wichita State University)

Friday, January 11, 2019 -
3:15pm to 4:15pm
119 Physics

The classification of compact Riemannian manifolds with positive or non-negative sectional curvature is a long-standing problem in Riemannian geometry. One successful approach has been the introduction of symmetries, and an important first case to understand is that of continuous abelian symmetries. In recent work with Escher, we obtained an equivariant diffeomorphism classification of closed, simply-connected non-negatively curved Riemannian manifolds admitting an isotropy-maximal torus action, with implications for the Maximal Symmetry Rank Conjecture for non-negatively curved manifolds. I will discuss joint work with Escher and Dong, that builds on this work to extend the classification to those manifolds admitting an almost isotropy-maximal action.

Last updated: 2020/01/25 - 10:35pm