Speaker
Jonathan Glöckle, Universität Regensburg
Abstract
An initial data set on a manifold M is a pair of a Riemannian metric g and a symmetric 2-tensor k. They arise in general relativity as induced Riemannian metric and induced second fundamental form on a spacelike (Cauchy) hypersurface M of a spacetime. For physical reasons it makes sense to consider those initial data sets that satisfy the dominant energy condition (=dec) — a condition that generalizes non-negative scalar curvature from the case k=0. In this talk I will explain how index theory for the Dirac-Witten operator can be used to establish non-connectivity of the space of initial data sets subject to strict dec.