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The APS-index and the spectral flow. (English) Zbl 1512.47022

The paper is a well-written, well-organized and well-illustrated contribution to the index theory of one-parameter families of self-adjoint Fredholm operators.
The authors extend the well-known equality at the level of one-parameter families of Riemannian, Lorentzian-Dirac operators between the APS index and spectral flow to abstract situations. The first case follows from using essentially [S. Azzali and C. Wahl, J. Topol. Anal. 3, No. 1, 37–67 (2011; Zbl 1216.58007), Theorem 2.1] and the second case follows from converting the two quantities into the relative index associated to spectral projections.

MSC:

47A53 (Semi-) Fredholm operators; index theories
58J20 Index theory and related fixed-point theorems on manifolds
58J30 Spectral flows
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References:

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