For a continuous curve of families of Dirac type operators we define a higher spectral flow as a K-group element.We show that this higher spectral flow can be computed analytically by η-forms, and is related to the family index in the same way as the spectral flow is related to the index.We also introduce a notion of Toeplitz family and relate its index to the higher spectral flow.
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Dai et al. (1996) studied this question.
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