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

Man Ho HO*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

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.

Original languageEnglish
Pages (from-to)941-987
Number of pages47
JournalJournal of Topology and Analysis
Volume12
Issue number4
DOIs
Publication statusPublished - 1 Dec 2020

Scopus Subject Areas

  • Analysis
  • Geometry and Topology

User-Defined Keywords

  • Bismut-Cheeger eta form
  • Cheeger-Chern-Simons class
  • local family index theorem
  • Riemann-Roch-Grothendieck theorem

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