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The index of a local boundary value problem for strongly Callias-type operators. (English) Zbl 1444.58005

Let \(M\) be a complete Riemannian manifold with non-compact boundary \(\partial M\). We assume that \(\partial M\) is a disjoint union of finitely many connected components. Then each connected component is a complete manifold without boundary. Let \(E\) be an (ungraded) Dirac bundle over \(M\) and let \(D\) denote the Dirac operator on \(E\). Let \(D_1=D+A\) be a formally self-adjoint Callias-type operator on \(M\). We impose slightly stronger conditions on the growth of the potential \(A\) and call the operators satisfying these conditions strongly Callias-type. In this interesting paper, the authors compute the index of a local boundary value problem for a strongly Callias-type operator \(D_1\) on \(M\). This index theorem extends an index theorem of \(D\). Freed to non-compact manifolds.

MSC:

58J20 Index theory and related fixed-point theorems on manifolds
58J28 Eta-invariants, Chern-Simons invariants
58J30 Spectral flows
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References:

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