A family resolvent cocycle and higher spectral flow

Aihui Sun; Jian Wang; Yong Wang

doi:10.4134/BKMS.b160601

Bulletin of the
Korean Mathematical Society BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

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Bull. Korean Math. Soc. 2017; 54(4): 1387-1407

Online first article June 28, 2017 Printed July 31, 2017

https://doi.org/10.4134/BKMS.b160601

A family resolvent cocycle and higher spectral flow

Aihui Sun, Jian Wang, and Yong Wang

Northeast Normal University, Tianjin University of Technology and Education, Northeast Normal University

Abstract

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Abstract

In this paper, we introduce a family resolvent cocycle and express the Chern Character of Dai-Zhang higher spectral flow as a pairing of a family resolvent cocycle and the odd Chern character of a unitary matrix, which generalize the odd index formula of Carey et al. to the family case.

Keywords: family resolvent cocycle, higher spectral flow

MSC numbers: 58B30, 46L87