Tue, November 25, 2014
1:45 pm - 2:45 pm
CH240
Title: Cohomology operations and positive sectional curvature
Speaker: Lee Kennard, UC Santa Barbara
Abstract: After discovering the relations among Steenrod powers that bear his name, J. Adem proved a theorem on singly generated cohomology rings. His line of reasoning eventually led to J.F. Adams' resolution of the Hopf invariant one problem. I will discuss a generalization of Adem's theorem and a different application of it to geometry. When combined with a fundamental result of B. Wilking, this result leads to computations of topological invariants of manifolds that admit Riemannian metrics with positive sectional curvature and symmetry.