On index formulas for manifolds with metric horns
نویسنده
چکیده
In this paper we discuss the index problem for geometric differential operators (Spin-Dirac operator, Gauß-Bonnet operator, Signature operator) on manifolds with metric horns. On singular manifolds these operators in general do not have unique closed extensions. But there always exist two extremal extensions Dmin and Dmax. We describe the quotient D(Dmax)/D(Dmin) explicitely in geometric resp. topologic terms of the base manifolds of the metric horns. We derive index formulas for the Spin-Dirac and Gauß-Bonnet operator. For the Signature operator we present a partial result.
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