Leírás
Előadó: Daniel Luckhardt
Cím: Benjamini-Schramm convergence of normalized characteristic numbers
Absztrakt: On the class of Riemannian manifolds with Ricci curvature and injectivity radius bounded from below we study the parameter given by a characteristic number over the volume of the manifold. The domain of this parameter is endowed with the Benjamini-Schramm (BS) topology induced by pointed Gromov-Hausdorff convergence. We give an exposition of a proof that this parameter is continuous and has a continuous extension to the completion of its domain in the BS topology. From the known fact that this completion is compact one can derive a testability result for characteristic numbers as well as a uniform bound on any fixed characteristic number in terms of the volume.