Mathematical Research Letters
Volume 3, Issue 1, January 1996 pp. 93-102.
Higher Spectral FlowAuthors: Xianzhe Dai and Weiping Zhang
Author institution: University of Southern California, and Nankai Institute of Mathematics
Summary: 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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