Coronas and Callias type operators in coarse geometry

Abstract

We interpret the coarse symbol and index class of a Callias type Dirac operator $D+\Psi$ on a manifold $M$ as a pairing between the coarse symbol and index classes associated to $D$ and K-theory classes of the coarse corona of $M$ or $M$ itself determined by $\Psi$. Local positivity of $D$ and local invertibility of $\Psi$ are incorporated in terms of support conditions on the $K$-theoretic level.