Asymptotic spectral flow for Dirac operators

Dirac Operators and Spectral Geometry

Discrete spectral triples converging to dirac operators

We exhibit a series of discrete spectral triples converging to the canonical spectral triple of a finite dimensional manifold. Thus we bypass the non-go theorem of Gökeler and Schücker. Sort of counterexample. In [2] Connes gave the most general example of non commutative manifolds defined from finite spectral triples, and such discrete manifolds were classified independently by Krajewsky [5, 6...

The h-invariant, Maslov index, and spectral flow for Dirac-type operators on manifolds with boundary

Several proofs have been published of the modZ gluing formula for the h-invariant of a Dirac operator. However, so far the integer contribution to the gluing formula for the h-invariant is left obscure in the literature. In this article we present a gluing formula for the h-invariant which expresses the integer contribution as a triple index involving the boundary conditions and the Calderón pr...

The η–invariant, Maslov index, and spectral flow for Dirac–type operators on manifolds with boundary

Several proofs have been published of the modZ gluing formula for the η–invariant of a Dirac operator. However, so far the integer contribution to the gluing formula for the η–invariant is left obscure in the literature. In this article we present a gluing formula for the η–invariant which expresses the integer contribution as a triple index involving the boundary conditions and the Calderón pr...

Spectral Bounds for Dirac Operators on Open Manifolds

We extend several classical eigenvalue estimates for Dirac operators on compact manifolds to noncompact, even incomplete manifolds. This includes Friedrich’s estimate for manifolds with positive scalar curvature as well as the author’s estimate on surfaces.