Jonathan Glöckle: Initial data sets and index theory

Date: 2023-07-12

Time: 10:40 - 11:05

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Jonathan Glöckle, Universität Regensburg


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.