About this Event
View map Free EventSpeaker: Lawrence Mouille, UC Riverside
Title: Maximal torus symmetry and intermediate Ricci curvatures
Abstract: The Grove-Searle maximal symmetry-rank theorem states that if a closed n-manifold has positive sectional curvature, then its symmetry-rank (the rank of its isometry group) is bounded above by $\lfloor (n+1)/2\rfloor$, and in the case of equality, the manifold is diffeomorphic to a quotient of a sphere. In this talk, I will show that a generalized bound on the symmetry-rank holds for manifolds with positive intermediate Ricci curvature, a condition on the curvature tensor that interpolates between having positive sectional curvature and having positive Ricci curvature. Furthermore, the argument is local in nature, only requiring the existence of locally-defined commuting Killing fields. I will outline a procedure for creating warped products that have maximal "local symmetry-rank", and show that any Riemannian manifold is $C^1$-close to one that has quasi-positive curvature and maximal "local symmetry-rank".
0 people are interested in this event
User Activity
No recent activity