# The local version of the Lorentzian index theorem

#### 30.11.2017, 16:15  –  Haus 9, Raum 1.10 Forschungsseminar Differentialgeometrie

Christian Bär

The Atiyah-Singer index theorem for Dirac operators D on compact Riemannian spin n-manifolds can be proved using the heat kernels of D*D and of DD*.  Namely, one easily sees that

<tex>\mathrm{ind}(D) = \mathrm{Tr}(e^{-tD^*D}) - \mathrm{Tr}(e^{-tDD^*})</tex>

for any t>0. Inserting the short time asymptotics