Positive scalar curvature and an equivariant Callias-type index theorem for proper actions (Q1982606)

A Callias-type operator on a complete Riemannian manifold is an operator of the form \(D + i\Phi\) where \(D\) is a Dirac operator and \(\Phi\) is a self-adjoint potential which commutes with the Clifford multiplication and satisfies certain growth conditions at infinity. By the celebrated Callias-type index theorem, the index of a Callias-type operator on a complete odd-dimensional manifold is equal to the index of a certain operator induced by \(\Phi\) on a compact hypersurface. In this nice paper, the authors prove an equivariant Callias-type index theorem for proper actions. Some interesting applications of this equivariant Callias-type index theorem are also given.