On the index formula for singular surfaces
The authors obtained the index formula for elliptic pseudodifferential operators on a 2-dimensional manifold with conical points which contains the Atiyah-Singer integral, the eta invariant and the other term expressed by the conormal principal and subprincipal symbols of the operator at the conical points. In this paper, they induce an explicit description of the contribution of a conical point for elliptic differential operators: By changing the origin in the complex plane they make the third term to vanish reducing the whole contribution of the conical point to the shifted eta invariant. They describe the eta invariant in terms of the monodromy index for an ordinary differential equation defined by the conormal symbol.
conical point for elliptic differential operators
scientific article; zbMATH DE number 1463727