Elliptic boundary value problem on non-compact $G$-manifolds

Abstract

In this paper, an equality between the Hochs-Mathai type index and the Atiyah-Patodi-Singer type index is established when the manifold and the group action are both non-compact, which generalizes a result of Ma and Zhang for compact group actions. As a technical preparation, a problem concerning the Fredholm property of the global elliptic boundary value problems of the Atiyah-Patodi-Singer type on a non-compact manifold is studied.

34 pages, 1 figure, various improvements according to referee's suggestion, to be published

References in corpus (2)

• Geometric quantization and families of inner products
• The index theory on non-compact manifolds with proper group action