| Résume | An elliptic differential operator on a complete manifold, which is invertible outside a compact set, is Fredholm and also admits a higher index in the K-theory of the $C^*$-algebra of the fundamental group. Interesting examples involve manifolds admitting a positive scalar curvature metric outside a compact set and also the Atiyah-Patodi-Singer index theory for manifold with boundary (attaching a cylindrical end). We propose an approach to obtain the APS-type formulas of the Fredholm index and its generalizations for this type of operators, as applications we obtain (equivariant) index formulas for Dirac type operators on manifolds with boundaries and with corners. |
