On index formulas for manifolds with metric horns
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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 $D_{min}$ and $D_{max}$. We describe the quotient ${\cal D}(D_{max}) / {\cal D}(D_{min})$ 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.
The first version of this paper was completed August 1995 at the University of Augsburg.
LaTeX, 37 pages. Final version from 20 Jan 1998, completely revised
LaTeX, 37 pages. Final version from 20 Jan 1998, completely revised