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journal of functional analysis 157, 432 469 (1998) Higher Spectral Flow

Summary: journal of functional analysis 157, 432 469 (1998)
Higher Spectral Flow
Xianzhe Dai*
Department of Mathematics, University of Southern California,
Los Angeles, California 90089
E-mail: xdaiÄmath.usc.edu
Weiping Zhang-
Nankai Institute of Mathematics, Tianjin, 300071, People's Republic of China
Received January 27, 1997; accepted March 25, 1998
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 '^ -forms and is related to the family index in the same way
as the spectral flow is related to the index. We introduce a notion of Toeplitz family
and relate its index to the higher spectral flow. Applications to family indices for
manifolds with boundary are also given. 1998 Academic Press
The spectral flow for a one parameter family of self adjoint Fredholm
operators is an integer that counts the net number of eigenvalues that
change sign. This notion is introduced by Atiyah Patodi Singer [APS1] in


Source: Akhmedov, Azer - Department of Mathematics, University of California at Santa Barbara


Collections: Mathematics