On index formulas for manifolds with metric horns. (English) Zbl 0906.58049

In this paper it is discussed 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 \(D_{\min}\) and \(D_{\max}\). The authors describe the quotient \({\mathcal D}(D_{\max})/{\mathcal D}(D_{\min})\) explicitly in geometric resp. topological terms of the base manifolds of the metric horns. Moreover, they derive index formulas for the spin-Dirac operator and for the Gauß-Bonnet operator. Some partial results are presented for the signature operator.


58J20 Index theory and related fixed-point theorems on manifolds
58J05 Elliptic equations on manifolds, general theory
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