TY - JOUR
T1 - Local index theory and the Riemann-Roch-Grothendieck theorem for complex flat vector bundles
AU - Ho, Man Ho
N1 - Funding Information:
This research was supported by ISF grant 326/16 and GIF grant 1261/14.
PY - 2020/12/1
Y1 - 2020/12/1
N2 - 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.
AB - 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.
KW - Bismut-Cheeger eta form
KW - Cheeger-Chern-Simons class
KW - local family index theorem
KW - Riemann-Roch-Grothendieck theorem
UR - http://www.scopus.com/inward/record.url?scp=85058191943&partnerID=8YFLogxK
U2 - 10.1142/S1793525319500699
DO - 10.1142/S1793525319500699
M3 - Journal article
AN - SCOPUS:85058191943
SN - 1793-5253
VL - 12
SP - 941
EP - 987
JO - Journal of Topology and Analysis
JF - Journal of Topology and Analysis
IS - 4
ER -