New York Journal of Mathematics
Volume 29 (2023), 1496-1530


Man-Ho Ho

An extended variational formula for the Bismut--Cheeger eta form and its applications

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Published: December 27, 2023.
Keywords: Riemann--Roch--Grothendieck theorem, analytic index, Bismut--Cheeger eta form, differential K-theory.
Subject [2020]: Primary 19K56, 19L50, 19L10.

The purpose of this paper is to extend our previous work on the variational formula for the Bismut--Cheeger eta form without the kernel bundle assumption by allowing the spinc Dirac operators to be twisted by isomorphic vector bundles and to establish the Z2-graded additivity of the Bismut--Cheeger eta form. Using these results, we give alternative proofs of the fact that the analytic index in differential K-theory is a well defined group homomorphism and the Riemann--Roch--Grothendieck theorem in R/Z K-theory.


The author would like to thank Steve Rosenberg for his comments and suggestions for this paper, and Jonathan Kin-Yue Lee, where the idea of Proposition 4.4 is due to him. The author would also like to thank the referee for the helpful comments.

Author information

Man-Ho Ho
Hong Kong