Covering Spectra of Riemannian manifolds and Metric spaces

Christina Sormani, CUNY Lehman

Abstract: The talk will survey joint work with Wei on the notion of a covering spectrum of a Riemannian manifold and its relationship with the existence of a universal cover and the length spactrum. We close with a new proposed rescaled covering spectrum which should capture the geometric topological behavior at infinity. A few possible definitions can be made and we are curious which might be the most useful to the study of the asymptotic geometry of groups. This is all joint work with Guofang Wei (UCSB).