Scalar curvature is a local invariant of a Riemannian manifold. It measures asymptotically the volume growth of geodesic balls. Understanding the topological space of all positive scalar curvature metrics on a closed manifold has been an active field of study during the last 30 years. So far, these spaces have been considered from an isotopy viewpoint.
I will describe a new approach to study this space bases on the notion of concordance. To this end, I construct with the help of cubical set theory a comparison space that only encodes concordance information and in which the space of psc metrics canonically embeds. After the presentation of some of its properties I will show that the indexdifference, the most important invariant in this field, factors over the comparison space and draw conclusions.
|Où?||PER 07 1.311
Chemin du Musée 6
|Intervenants||Thorsten Hertl (Uni. Göttingen)|