A Callias-type index theorem with degenerate potentials

Abstract

A generalization of Callias' index theorem for self adjoint Dirac operators with skew adjoint potentials on asymptotically conic manifolds is presented in which the potential term may have constant rank nullspace at infinity. The index obtained depends on the choice of a family of Fredholm extensions, though as in the classical version it depends only on the data at infinity.

42 pages. v1 is superseded by v3 and arXiv:1310.2974, v4, v5 incorporate revisions from referee reports. To appear in Comm. PDE

References in corpus (1)

• Dimension of monopoles on asymptotically conic 3-manifolds

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• Callias-type operators in $C^{\ast }$-algebras and positive scalar curvature on noncompact manifolds
• Low energy limit for the resolvent of some fibered boundary operators
• Generalised Dirac-Schrödinger operators and the Callias Theorem
• An $L^2$-index formula of monopoles with Dirac-type singularities
• A hyper-Kähler metric on the moduli spaces of monopoles with arbitrary symmetry breaking