APS index theorem for even-dimensional manifolds with non-compact boundary

Abstract

We study the index of the APS boundary value problem for a strongly Callias-type operator $D$ on a complete even dimensional Riemannian manifold $M$ (the odd dimensional case was considered in our previous paper arXiv:1706.06737). We use this index to define the relative $\eta$-invariant $\eta (A_1,A_0)$ of two strongly Callias-type operators, which are equal outside of a compact set. Even though in our situation the $\eta$-invariants of $A_1$ and $A_0$ are not defined, the relative $\eta$-invariant behaves as if it were the difference $\eta (A_1)-\eta (A_0)$. We also define the spectral flow of a family of such operators and use it compute the variation of the relative $\eta$-invariant.

to appear in Communications in Analysis and Geometry. arXiv admin note: substantial text overlap with arXiv:1706.06737

References in corpus (2)

• An index theorem for Lorentzian manifolds with compact spacelike Cauchy boundary
• The Atiyah-Patodi-Singer index on manifolds with non-compact boundary

Cited by in corpus (1)

• Cauchy data spaces and Atiyah-Patodi-Singer index on non-compact manifolds