ON INDEX FORMULAS FOR MANIFOLDS WITH METRIC HORNS

In this paper we discuss the index problem for geometric differential operators (Spin-Dirac operator, Gauss-Bonnet operator, Signature opera tor) on manifolds with metric horns. On singular manifolds these opera tors in general do not have unique closed extensions. But there always exist two extremal extensions D-min and D-max. We describe the quotie nt D(D-max)/D(D-min) explicitely in geometric resp. topological terms of the base manifolds of the metric horns. We derive index formulas fo r the Spin-Dirac and Gauss-Bonnet operator. For the Signature operator we present a partial result.