Document Type

Journal Article

Department/Unit

Department of Mathematics

Title

Local index theory and the Riemann–Roch–Grothendieck theorem for complex flat vector bundles

Language

English

Abstract

The purpose of this paper is to give a proof of the real part of the Riemann–Roch–Grothendieck theorem for complex flat vector bundles at the differential form level in the even dimensional fiber case. The proof is, roughly speaking, an application of the local family index theorem for a perturbed twisted spin Dirac operator, a variational formula of the Bismut–Cheeger eta form without the kernel bundle assumption in the even dimensional fiber case, and some properties of the Cheeger–Chern–Simons class of complex flat vector bundle.

Keywords

Riemann–Roch–Grothendieck theorem, Cheeger–Chern–Simons class, Cheeger–Chern–Simons class, local family index theorem, Bismut–Cheeger eta form

Publication Date

2018

Source Publication Title

Journal of Topology and Analysis

Publisher

World Scientific Publishing

DOI

10.1142/S1793525319500699

Link to Publisher's Edition

https://doi.org/10.1142/S1793525319500699

ISSN (print)

17935253

ISSN (electronic)

17937167

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