Torus actions and positive curvature
Lee Kennard (Syracuse University)
Abstract: In the 1930s, H. Hopf conjectured that an even-dimensional Riemannian manifold with positive sectional curvature has positive Euler characteristic. In joint work with M. Wiemeler and B. Wilking, this is confirmed in the special case where the isometry group has rank at least five. Previous results of this form required the rank to grow to infinity as a function of the manifold dimension. The main new tool is a structural result for representations of tori with the special property that all isotropy groups are connected. Such representations are surprisingly rigid, and we analyze them using only elementary techniques.
differential geometrygeometric topologymetric geometry
Audience: researchers in the topic
Virtual seminar on geometry with symmetries
Series comments: Description: Research seminar in Lie group actions in Riemannian geometry.
The seminar meets every other Wednesday. To accommodate most time zones, the time rotates. The Zoom link is sent to the mailing list around 24 hours before each talk. To subscribe to the mailing list, send a message to geometrywithsymmetries@gmail.com requiring it.
Organizers: | Fernando Galaz-GarcĂa*, Carolyn Gordon, Ramiro Lafuente*, Emilio Lauret* |
*contact for this listing |