Mathematical Research Letters

Volume 3 (1996)

Number 1

Higher Spectral Flow

Pages: 93 – 102



Xianzhe Dai (University of Southern California)

Weiping Zhang (Nankai Institute of Mathematics)


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 $\hat{\eta}$-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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