HIGHER SPECTRAL FLOW

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 s pectral flow can be computed analytically by <(eta)over cap>-forms and is related to the family index in the same way as thr spectral flow i s related to the index. We introduce a notion of Toeplitz family and r elate its index to the higher spectral flow. Applications to family in dices for manifolds with boundary are also given. (C) 1998 Academic Pr ess.