On index formulas for manifolds with metric horns

Lesch, M.; Peyerimhoff, N.

Abstract

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 of their domains explicitely in geometric resp. topological 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.

Citation

Lesch, M., & Peyerimhoff, N. (1998). On index formulas for manifolds with metric horns. Communications in Partial Differential Equations, 23(3 & 4), 649-684

• Journal Article Type: Article
• Publication Date: 1998
• Journal: Communications in Partial Differential Equations
• Print ISSN: 0360-5302
• Publisher: Taylor and Francis Group
• Peer Reviewed: Peer Reviewed
• Volume: 23
• Issue: 3 & 4
• Pages: 649-684