Dirac operators on foliations

30.06.2016, 16:15 Uhr  –  Campus Golm, Haus 9, Raum 0.14
Forschungsseminar Differentialgeometrie

Ken Richardson

Given a foliation on a closed Riemannian manifold, the transversal Dirac operator is a Dirac operator that differentiates only in the directions normal to the foliation and is thereby transversally elliptic. This operator has nice properties and a well-defined index when the metric is bundle-like --- that is, when the foliation locally has the structure of a Riemannian submersion. We will show some standard techniques used to do analysis on these operators and discuss some known results. The talk will contain some joint work with G. Habib and with F. W. Kamber and J. Brüning.