Thorsten Hertl:
Concordances in Positive Scalar Curvature and Index Theory
Time and place
Monday, 7.11.22, 16:15-17:15, Hörsaal II, Albertstr. 23b
Abstract
Scalar curvature is a local invariant of a Riemannian manifold. It measures\nasymptotically the volume growth of geodesic balls. Understanding the topological space of\nall positive scalar curvature metrics on a closed manifold has been an active field of study\nduring the last 30 years. So far, these spaces have been considered from an isotopy\nviewpoint. I will describe a new approach to study this space based on the notion of\nconcordance. To this end, I construct with the help of cubical set theory a comparison space\nthat only encodes concordance information and in which the space of positive scalar\ncurvature metrics canonically embeds. After the presentation of some of its properties, I will\nshow that the indexdifference factors over the comparison space using a new model of real\nK-theory that is based on pseudo Dirac operators.